Books


  • T. Heister and L. Rebholz, Scientific Computing for Scientists and Engineers, Second Edition De Gruyter (Berlin), 2023. Book webpage


  • T. Heister, L. Rebholz and F. Xue, Numerical Analysis: An Introduction, De Gruyter (Berlin), 2019. Book webpage


  • T. Heister and L. Rebholz, Scientific Computing for Scientists and Engineers, De Gruyter (Berlin), 2015. ISBN 978-3-11-035942-8.


  • W. Layton and L. Rebholz, Approximate Deconvolution Models of Turbulence: Analysis, Phenomenology and Numerical Analysis, Springer(Verlag), 2012, ISBN 978-3-642-24408-7. Book's webpage


    • Papers


    Links provided to journal websites. If you don't have access, send me an email and I will send you a preprint.

    In Review


  • S. Pollock, L. Rebholz, X. Tu and M. Xiao, Analysis of the Picard-Newton iteration for the Navier-Stokes equations: global stability and quadratic convergence, submitted. arxiv


  • M. Dallas, S. Pollock and L. Rebholz, Analysis of an Adaptive Safeguarded Newton-Anderson Algorithm with Applications to Fluid Problems, submitted. arxiv


  • A. Diegel, X. Li and L. Rebholz, Analysis of continuous data assimilation with large (or even infinite) nudging parameters, submitted.


    • In Press


    2024


  • B. Garcia-Archilla, X. Li, J. Novo and L. Rebholz, Enhancing nonlinear solvers for the Navier-Stokes equations with continuous (noisy) data assimilation, Computer Methods in Applied Mechanics and Engineering, 424, 116903, 1-15, 2024. arxiv


  • M. Akbas, A. Diegel and L. Rebholz, Continuous data assimilation of a discretized barotropic vorticity model of geophysical flow, Computers and Mathematics with Applications, 160, 30-45, 2024.


  • J. Liu, L. Rebholz and M. Xiao, Efficient and effective algebraic splitting iterations for nonlinear saddle point problems, Mathematical Methods in the Applied Sciences, 47, 451-474, 2024. Download


  • E. Hawkins, L. Rebholz and D. Vargun, Removing splitting/modeling error in projection/penalty methods for Navier-Stokes simulations with continuous data assimilation, Communications in Mathematical Research, 40(1), 1-29, 2024. arxiv preprint


  • M. Olshanskii and L. Rebholz, Local conservation laws of continuous Galerkin method for the incompressible Navier–Stokes equations in EMAC form, Computer Methods in Applied Mechanics and Engineering, 418B, 116583, 1-14, 2024. arxiv preprint Journal Download


    • 2023


  • X. Li, E. Hawkins*, L. Rebholz and D. Vargun*, Accelerating and enabling convergence of nonlinear solvers for Navier-Stokes equations by continuous data assimilation, Computer Methods in Applied Mechanics and Engineering, 416 (116313), 1-17, 2023. Journal Download .


  • L. Rebholz and M. Xiao, The effect of Anderson acceleration on the convergence order of superlinear and sublinear nonlinear solvers, Journal of Scientific Computing, 96(34), 1-23, 2023. Journal Download


  • S. Pollock, L. Rebholz and D. Vargun, An efficient nonlinear solver and convergence analysis for a viscoplastic flow model, Numerical Methods for Partial Differential Equations, 39:3874-3896, 2023. arxiv preprint Journal Download


  • S. Pollock and L. Rebholz, Filtering for Anderson acceleration, SIAM Journal on Scientific Computing, 45(4), A1571-A1590, 2023. arxiv preprint Journal Download


  • L. Rebholz and F. Tone, Long-time $H^1$-stability of BDF2 time stepping for 2D Navier-Stokes equations, Applied Mathematics Letters, 141, 108624, 1-8, 2023. Journal Download


  • S. Ingimarson, M. Neda, L. Rebholz, J. Reyes and A. Vu, Improved long time accuracy for projection methods for Navier-Stokes equations using EMAC formulation, International Journal of Numerical Analysis and Modeling, 20(2), 176-198, 2023.


  • P. Guven Geredeli, L. Rebholz, D. Vargun and A. Zytoon, Improved convergence of the Arrow-Hurwicz iteration for the Navier-Stokes equation via grad-div stabilization and Anderson acceleration, Journal of Computational and Applied Mathematics, 422, 114920, 1-16, 2023.


    • 2022


  • S. Ingimarson, L. Rebholz and T. Iliescu, Full and reduced order model consistency of the nonlinearity discretization in incompressible flows, Computer Methods in Applied Mechanics and Engineering, 401B, 115620, 1-16, 2022. Download


  • M. Mohebujjaman, H. Wang, L. Rebholz and M.A.A. Mahbub, An efficient algorithm for simulating ensembles of parameterized MHD flow problems, Computers and Mathematics with Applications, 112, 167-180, 2022. arxiv preprint Journal Download


  • A. Diegel and L. Rebholz, Continuous data assimilation and long-time accuracy in a C0 interior penalty method for the Cahn-Hilliard equation, Applied Mathematics and Computation, 424 (127042), 1-22, 2022. Arxiv preprint Journal Download


  • Y. Zhang, A. Palha, M. Gerritsma and L. Rebholz, A mass-, kinetic energy- and helicity-conserving mimetic dual-field discretization for three-dimensional incompressible Navier-Stokes equations, part I: Periodic domains, Journal of Computational Physics, 451, 110868, 1-23, 2022. Arxiv preprint Journal Download


    • 2021


  • S. Pollock, L. Rebholz and M. Xiao, Acceleration of nonlinear solvers for natural convection problems, Journal of Numerical Mathematics, 29(4), 1-19, 2021. Arxiv preprint


  • L. Rebholz, D. Vargun and M. Xiao, Enabling fast convergence of the iterated penalty Picard iteration with $O(1)$ penalty parameter for incompressible Navier-Stokes via Anderson acceleration, Computer Methods in Applied Mechanics and Engineering, 387 (114178), 1-17, 2021. Arxiv preprint Journal Download


  • S. Pollock and L. Rebholz, Anderson acceleration for contractive and noncontractive operators, IMA Journal of Numerical Analysis, 41 (4), 2841-2872, 2021. Arxiv preprint Journal Download


  • D. Forbes, L. Rebholz and F. Xue, Anderson acceleration of nonlinear solvers for the stationary Gross-Pitaevskii equation, Advances in Applied Mathematics and Mechanics, 13, 1096-1125, 2021. preprint Journal download


  • M. Gardner, A. Larios, L. Rebholz, D. Vargun and C. Zerfas, Continuous data assimilation applied to a velocity-vorticity formulation of the 2D Navier-Stokes equations, American Institute of Mathematical Sciences Electronic Research Archive, 29(3): 2223-2247, 2021. Arxiv preprint


  • L. Rebholz and C. Zerfas, Simple and efficient continuous data assimilation of evolution equations via algebraic nudging, Numerical Methods for Partial Differential Equations, 37 (3), 2588-2612, 2021. Arxiv preprint Journal Download


  • M. Akbas and L. Rebholz, Modular grad-div stabilization for incompressible non-isothermal fluid flows, Applied Mathematics and Computation, 393 (125748), 1-18, 2021. Arxiv preprint Journal Download


  • C. Mou, B. Koc, O. San, L. Rebholz, T. Iliescu, Data-driven variational multiscale reduced order models, Computer Methods in Applied Mechanics and Engineering, 373 (113470), 1-36, 2021. Journal Download Arxiv preprint


    • 2020


  • M. A. Olshanskii and L. Rebholz, Longer time accuracy for incompressible Navier-Stokes simulations with the EMAC formulation, Computer Methods in Applied Mechanics and Engineering, 372(113369), 1-17, 2020. Arxiv preprint Download


  • C. Evans, S. Pollock, L. Rebholz and M. Xiao, A proof that Anderson acceleration increases the convergence rate in linearly converging fixed point methods (but not in quadratically converging ones), SIAM Journal on Numerical Analysis, 58(1), 788-810, 2020. Arxiv preprint Download


  • L. Rebholz, A. Viguerie and M. Xiao, Analysis of Algebraic Chorin Temam splitting for incompressible NSE and comparison to Yosida methods, Journal of Computational and Applied Mathematics,365, 112366, 2020. Download


    • 2019


  • F. Eroglu, S. Kaya, and L. Rebholz, POD-ROM for the Darcy-Brinkman Equations with Double-Diffusive Convection, Journal of Numerical Mathematics, 27(3), 123-139, 2019. Download


  • C. Zerfas, L. Rebholz, M. Schneier and T. Iliescu, Continuous data assimilation reduced order models of fluid flow, Computer Methods in Applied Mechanics and Engineering, 357, 112596, 1-21, 2019. arxiv Download


  • S. Pollock, L. Rebholz and M. Xiao, Anderson-accelerated convergence of Picard iterations for incompressible Navier-Stokes equations, SIAM Journal on Numerical Analysis, 57(2), 615-637, 2019. Arxiv preprint Journal Download


  • L. Rebholz, A. Viguerie and M. Xiao, Efficient nonlinear iteration schemes based on algebraic splitting for the incompressible Navier-Stokes equations, Math. Comp., 88, 1533-1557, 2019. Download


  • A. Linke and L. Rebholz, Pressure-induced locking in mixed methods for the time-dependent (Navier-)Stokes equations, Journal of Computational Physics, 388, 350-356, 2019. Download


  • F. Eroglu, S. Kaya, and L. Rebholz, Decoupled Modular Regularized VMS-POD for Darcy-Brinkman Equations, IAENG International Journal of Applied Mathematics,, 49 (2),134-144, 2019. Download


  • L. Rebholz, D. Wang, Z. Wang, K. Zhao, and C. Zerfas, Initial Boundary Value Problems for a System of Parabolic Conservation Laws Arising From Chemotaxis in Multi-Dimensions, DCDS-A, 39(7), 3789-3838, 2019. Download


  • S. Charnyi, T. Heister, M. Olshanskii and L. Rebholz, Efficient discretizations for the EMAC formulation of the incompressible Navier-Stokes equations, Applied Numerical Mathematics, 141, 220-233, 2019. Download at journal, arxiv


  • A. Larios, L. Rebholz and C. Zerfas, Global in time stability and accuracy of IMEX-FEM data assimilation schemes for Navier-Stokes equations Computer Methods in Applied Mechanics and Engineering, 345, 1077-1093, 2019. Download at journal , arxiv


  • A. Larios, Y. Pei and L. Rebholz, Global well-posedness of the velocity-vorticity-Voigt model of the 3D Navier-Stokes equations, Journal of Differential Equations , 266(5), 2435-2465, 2019. Arxiv journal download


  • T. Iliescu, M. Mohebujjaman and L. Rebholz, Physically-Constrained Data-Driven Correction for Reduced Order Modeling of Fluid Flows, International Journal of Numerical Methods in Fluids, 89, 103-122, 2019. Download


  • L. Bertagna, A. Quaini, L.G. Rebholz, A. Veneziani, On the sensitivity to the filtering radius in Leray models of incompressible flow, in Contributions to Partial Differential Equations and Applications - Computational Methods in the Applied Sciences 47, 111-130, editors: B.N Chetverushkin, W. Fitzgibbon, Y.A. Kuznetsov, P. Neittaanmäki, J. Periaux, J. and O. Pironneau, Springer International, 2019.


    • 2018


  • M. Akbas, A. Linke, L. Rebholz and P. Schroeder, The analogue of grad-div stabilization in DG methods for incompressible flows: limiting behavior and extension to tensor-product meshes, Computer Methods in Applied Mechanics and Engineering, 341, 917-938, 2018. Arxiv journal download


  • F. Eroglu, S. Kaya and L. Rebholz, A numerical investigation of the VMS-POD model for Darcy-Brinkman equations, Proceedings of the World Congress on Engineering, volume I, 1-5, 2018. Download


  • X. Xie, M. Mohebujjaman, L. Rebholz and T. Iliescu, Data-Driven Filtered Reduced Order Modeling Of Fluid Flows, SIAM Journal on Scientific Computing, 40(3), B834-B857, (2018). Download


  • M. Olshanskii, L. Rebholz, and A. Salgado, On well-posedness of a velocity-vorticity formulation of the Navier-Stokes equations with no-slip boundary conditions, DCDS-A, 38(7), 3459-3477, 2018. Arxiv


  • L. Rebholz, S.M. Wise, and M. Xiao, Penalty-Projection Schemes for the Cahn-Hilliard Navier-Stokes Diffuse Interface Model of Two Phase Flow, and their Connection to Divergence-Free Coupled Schemes, International Journal on Numerical Analysis and Modeling, 15(4), 649-676, 2018. Download


  • M. Akbas, L. Rebholz and C. Zerfas, Optimal vorticity accuracy in an efficient velocity-vorticity method for the 2D Navier-Stokes equations, Calcolo, 55(3), 1-29, 2018. Download


    • 2017


  • A. Linke, M. Neilan, L. Rebholz and N. Wilson, A connection between coupled and penalty projection timestepping schemes with FE spatial discretization for the Navier-Stokes equations, Journal of Numerical Mathematics, 25(4), 229-248, 2017. Download


  • L. Rebholz and M. Xiao, Improved accuracy in algebraic splitting methods for Navier-Stokes equations, SIAM Journal on Scientific Computing, 39(4), A1489-A1513, 2017. Download


  • L. Rebholz, C. Zerfas and K. Zhao, Global in time analysis and sensitivity analysis for the reduced NS-$\alpha$ model of incompressible flow, Journal of Mathematical Fluid Mechanics, 19(3), 445-467, 2017. Download


  • V. John, A. Linke, C. Merdon, M. Neilan and L. Rebholz, On the divergence constraint in mixed finite element methods for incompressible flows, SIAM Review, 59(3), 492–544, 2017. Download


  • F. Eroglu, S. Kaya, and L. Rebholz, A Modular Regularized Variational Multiscale Proper Orthogonal Decomposition for Incompressible Flows, Computer Methods in Applied Mechanics and Engineering, 325, 350-368, 2017. Download


  • M. Mohebujjaman, L. Rebholz, X. Xie, and T. Iliescu, Energy balance and mass conservation in reduced order models of fluid flows, Journal of Computational Physics, 346, 262-277, 2017. Download


  • M. Akbas, S. Kaya and L. Rebholz, On the stability at all times of linearly extrapolated BDF2 timestepping for multiphysics incompressible flow problems, Numerical Methods for Partial Differential Equations, 33(4), 995-1017, 2017. Download


  • M. Akbas, M. Mohebujjaman, L. Rebholz and M. Xiao, High order algebraic splitting for magnetohydrodynamics simulation, Journal of Computational and Applied Mathematics, 321, 128-142, 2017. Download


  • A. Bowers and L. Rebholz, The reduced NS-$\alpha$ model for incompressible flow: a review of recent progress, Fluids, 2 (38), 1-20, 2017. Download


  • T. Heister, M. Mohebujjaman and L. Rebholz, Decoupled, unconditionally stable, higher order discretizations for MHD flow simulation, Journal of Scientific Computing, 71(1), 21-43, 2017. Download


  • S. Charnyi, T. Heister, M. Olshanskii, and L. Rebholz, On conservation laws of Navier-Stokes Galerkin discretizations, Journal of Computational Physics, 337, 289-308, 2017. Download


  • T. Heister, M.A. Olshanskii and L. Rebholz, Unconditional long-time stability of a velocity-vorticity method for the 2D Navier-Stokes equations, Numerische Mathematik, 135, 143-167, 2017. Download


  • L. Rebholz, T.-Y. Kim and Young-Li Byon, On an accurate $\alpha$ model for coarse mesh turbulent channel flow simulation, Applied Mathematical Modelling, 43, 139-154, 2017. Download


  • M. Mohebujjaman and L. Rebholz, An efficient algorithm for computation of MHD flow ensembles, Computational Methods in Applied Mathematics, 17(1), 121-137, 2017. Download


    • 2016


  • M. Neda, F. Pahlevani, L. Rebholz and J. Waters, Sensitivity analysis of the grad-div stabilization parameter in finite element simulations of incompressible flow, Journal of Numerical Mathematics, 24(3), 189-206, 2016. Download


  • N. Jiang, M. Mohebujjaman, L. Rebholz and C. Trenchea, An optimally accurate discrete regularization for second order timestepping methods for Navier-Stokes equations, Computer Methods in Applied Mechanics and Engineering, 310, 388-405, 2016. Download


  • Y. Cao, S. Chen, and L. Rebholz, Well-posedness and a numerical study of a regularization model with adaptive nonlinear filtering for incompressible fluid flow, Computers and Mathematics with Applications, 71(11), 2192–2205, 2016.. Download


  • M. Akbas, S. Kaya and L. Rebholz, Numerical Studies on a Second Order Explicitly Decoupled Variational Multiscale Method, Numerical Mathematics and Advanced Concepts - ENUMATH 2015, edited by: B. Karasozen, M. Manguoglu, M. Tezer-Sezgin, S. Goktepe and U. Omur, Springer Lecture Notes in Computational Science and Engineering, volume 112, 2016.


  • M. Morales Hernandez, L. Rebholz, C. Tone and F. Tone, On the Stability of the Crank--Nicolson--Adams--Bashforth Scheme for the 2d Leray-alpha model, Numerical Methods for Partial Differential Equations, 32(4), 1155-1183, 2016. Download


  • L. Berselli, T.-Y. Kim, and L. Rebholz, Analysis of a reduced-order approximate deconvolution model and its interpretation as a Navier-Stokes-Voigt regularization, DCDS-B, 21(4), 1027-1050, 2016. Download


  • T. Heister, L. Rebholz and M. Xiao, Flux-preserving enforcement of inhomogeneous Dirichlet boundary conditions for strongly divergence-free mixed finite element methods for flow problems, Journal of Mathematical Analysis and Applications, 438(1), 507-513, 2016. Download


  • M. Akbas, S. Kaya, M. Mohebujjaman and L. Rebholz, Numerical analysis and testing of a fully discrete, decoupled penalty-projection algorithm for MHD in Elsasser variable, International Journal of Numerical Analysis and Modeling, 13(1), 90-113, 2016. Download


    • 2015


  • A. Dunca, T.-Y. Kim, L. Rebholz and E. Fried, Energy analysis and improved regularity estimates for multiscale deconvolution models of incompressible flow, Mathematical Methods in the Applied Sciences, 38(17), 4199-4209, 2015. Download


  • T. Heister, M. Olshanskii, L. Rebholz, and K. Galvin, Natural vorticity boundary conditions on solid walls, Computer Methods in Applied Mechanics and Engineering, 297, 18-37, 2015. Download


  • I. Monteiro, C. Manica, and L. Rebholz, Numerical study of a regularized barotropic vorticity model of geophysical flow, Numerical Methods for Partial Differential Equations, 31(5), 1492-1514, 2015. Download


  • L. Rebholz and M. Xiao, On reducing the splitting error in Yosida methods for the Navier-Stokes equations with grad-div stabilization, Computer Methods in Applied Mechanics and Engineering, 294, 259-277, 2015. Download


  • V. Cuff, A. Dunca, C. Manica and L. Rebholz, The reduced order NS-$\alpha$ model for incompressible flow: theory, numerical analysis and benchmark testing, ESAIM: Mathematical Modelling and Numerical Analysis (M2AN), 49(3), 641-662, 2015. Download


  • S. Le Borne and L. Rebholz, Preconditioning sparse grad-div/augmented Lagrangian stabilized saddle point systems, Computing and Visualization in Science, 16(6), 259-269, 2015. Download


  • M. Akbas, L. Rebholz, and F. Tone, A note on the importance of mass conservation in long-time stability of Navier-Stokes simulations using finite elements, Applied Mathematics Letters, 45, 98-102, 2015. Download


  • M. Belenli, S. Kaya, and L. Rebholz, An explicitly decoupled variational multiscale method for incompressible, non-isothermal flows, Computational Methods in Applied Mathematics, 15(1), 1-20, 2015. Download


  • M. Morales Hernandez and L. Rebholz, A note on helicity conservation in Leray models of incompressible flow, Journal of Mathematical Analysis and Applications, 422(1), 776-781, 2015. Download


    • 2014


  • S. Kaya, C. Manica and L. Rebholz, On Crank-Nicolson Adams-Bashforth timestepping for approximate deconvolution models in two dimensions, Applied Mathematics and Computation, 246, 23-38, 2014. Download


  • E. Jenkins, V. John, A. Linke and L. Rebholz, On the parameter choice in grad-div stabilization for incompressible flow problems, Advances in Computational Mathematics, 40(2), 491-516, 2014. Download


  • A. Bowers, S. Le Borne, and L. Rebholz, Error analysis and iterative solvers for Navier-Stokes projection methods with standard and sparse grad-div stabilization, Computer Methods in Applied Mechanics and Engineering, 275, 1-19, 2014. Download


  • K. Galvin, L. Rebholz, and C. Trenchea, Efficient, unconditionally stable, and optimally accurate FE algorithms for approximate deconvolution models, SIAM Journal on Numerical Analysis, 52(2), 678-707, 2014. Download


  • L. Rebholz and S. Watro, A note on Taylor-eddy and Kavosnay solutions of NS-$\alpha$-deconvolution and Leray-$\alpha$-deconvolution models, Journal of Nonlinear Dynamics, Volume 2014, ID 959038, 2014. Download


    • 2013


  • A. Dunca, M. Neda, and L. Rebholz, A mathematical and numerical study of a filtering-based multiscale fluid model with nonlinear eddy viscosity, Computers and Mathematics with Applications, 66(6), 917-933, 2013. Download


  • M. Belenli, S. Kaya, L. Rebholz, and N. Wilson, A subgrid stabilization finite element method for incompressible magnetohydrodynamics, International Journal of Computer Mathematics, 90(7), 1506-1523, 2013. Download


  • W. Layton and L. Rebholz, On relaxation times in the Navier-Stokes-Voigt model, International Journal of Computational Fluid Dynamics, 27(3), 184-187, 2013. Download


  • L. Rebholz, Well-posedness of a reduced order approximate deconvolution turbulence model, Journal of Mathematical Analysis and Applications, 405(2), 738-741, 2013. Download


  • A. Linke and L. Rebholz, On a reduced sparsity stabilization of grad-div type for incompressible flow problems, Computer Methods in Applied Mechanics and Engineering, 261, 142-153, 2013. Download


  • B. Cousins, S. Le Borne, A. Linke, L. Rebholz, and Z. Wang, Efficient linear solvers for incompressible flow simulations using Scott-Vogelius finite elements, Numerical Methods for Partial Differential Equations, 29(4), 1217-1237, 2013. Download .


  • A. Bowers and L. Rebholz, Numerical study of a regularization model for incompressible flow with deconvolution-based adaptive nonlinear filtering, Computer Methods in Applied Mechanics and Engineering, 258, 1-12, 2013. Download


  • E. D'Agnillo and L. Rebholz, On the enforcement of discrete mass conservation in incompressible flow simulations with continuous velocity approximation, In: Recent Advances in Scientific Computing and Applications: Proceedings of the 8th International Conference on Scientific Computing and Applications, edited by: Jichun Li, Eric Macharro, and Hongtao Yang, AMS Contemporary Mathematics, volume 586, 2013.


  • A. Bowers, T.-Y. Kim, M. Neda, L. Rebholz, and E. Fried, The Leray-$\alpha\beta$-deconvolution model: energy analysis and numerical algorithms, Applied Mathematical Modelling, 37(3), 1225-1241, 2013. Download


    • 2012


  • A. Bowers, L. Rebholz, A. Takhirov, and C. Trenchea, Improved accuracy in regularization models of incompressible flow via adaptive nonlinear filtering, International Journal for Numerical Methods in Fluids, 70, 805-828, 2012. Download


  • M. Benzi, M.A. Olshanskii, L. Rebholz, and Z. Wang, Assessment of a vorticity based solver for the Navier-Stokes equations, Computer Methods in Applied Mechanics and Engineering, 247, 216-225, 2012. Download


  • P. Kuberry, A. Larios, L. Rebholz and N. Wilson, Numerical approximation of the Voigt regularization for incompressible Navier-Stokes and magnetohydrodynamic flows, Computers and Mathematics with Applications, 64(8), 2647-2662, 2012. Download


  • A. Dunca, K. Kohler, M. Neda and L. Rebholz, A mathematical and physical study of multiscale deconvolution models of turbulence, Mathematical Methods in the Applied Sciences, 35, 1205-1219, 2012. Download


  • K. Galvin, A. Linke, L. Rebholz, and N. Wilson, Stabilizing poor mass conservation in incompressible flow problems with large irrotational forcing and application to thermal convection, Computer Methods in Applied Mechanics and Engineering, 237, 166-176, 2012. Download


  • W. Layton, L. Rebholz, and C. Trenchea, Modular nonlinear filter stabilization of methods for higher Reynolds numbers flow, Journal of Mathematical Fluid Mechanics, 14(2), 325-354, 2012. Download


  • T.-Y. Kim, L. Rebholz, and E. Fried, A deconvolution enhancement of the Navier-Stokes-alphabeta model, Journal of Computational Physics, 231(11), 4015-4027, 2012. Download


  • A. Bowers and L. Rebholz, Increasing accuracy and efficiency in FE computations of the Leray-deconvolution model, Numerical Methods for Partial Differential Equations, 28(2), 720-736, 2012. Download


  • K. Galvin, H.K. Lee, and L. Rebholz, Approximation of viscoelastic flows with defective boundary conditions, Journal of Non-Newtonian Fluid Mechanics, 169-170, 104-113, 2012 . Download .


    • 2011


  • M.A. Olshanskii and L. Rebholz, Application of barycenter refined meshes in linear elasticity and incompressible fluid dynamics, ETNA: Electronic Transactions in Numerical Analysis, 38, 258-274, 2011. Download


  • K. Galvin, H.K. Lee and L. Rebholz, A Numerical Study for a Velocity-Vorticity-Helicity formulation of the 3D Time-Dependent NSE, International Journal of Numerical Analysis and Modeling, Series B, 2(4), 355-368, 2011. Download


  • J. Connors, E. Jenkins, and L. Rebholz, On small-scale divergence penalization for incompressible flow problems via time relaxation, International Journal of Computer Mathematics, 88(15), 3202-3216, 2011. Download


  • B. Cousins, L. Rebholz, and N. Wilson, Enforcing energy, helicity and strong mass conservation in FE computations for incompressible Navier-Stokes simulations, Applied Mathematics and Computation, 281, 1208-1221, 2011. Download


  • M. Case, V. Ervin, A. Linke and L. Rebholz, A connection between Scott-Vogelius elements and grad-div stabilization, SIAM Journal on Numerical Analysis, 49(4), 1461-1481, 2011. Download


  • T.-Y. Kim, M. Neda, L. Rebholz, and E. Fried, A numerical study of the Navier-Stokes-$\alpha\beta$ model, Computer Methods in Applied Mechanics and Engineering, 200(41-44), 2891-2902, 2011. Download


  • A. Linke, L. Rebholz, and N. Wilson, On the convergence rate of grad-div stabilized Taylor-Hood to Scott-Vogelius solutions for incompressible flow problems, Journal of Mathematical Analysis and Applications, 381, 612-626, 2011. Download


  • H.K. Lee, M.A. Olshanskii, and L. Rebholz, On error analysis for the 3D Navier-Stokes equations in Velocity-Vorticity-Helicity form, SIAM Journal on Numerical Analysis, 49(2), 711-732, 2011. Download


  • C. Manica, M. Neda, M.A. Olshanskii, L. Rebholz, and N. Wilson, On an efficient finite element method for Navier-Stokes-omega with strong mass conservation, Computational Methods in Applied Mathematics, 11(1), 3-22, 2011. Download


  • C. Manica, M. Neda, M.A. Olshanskii and L. Rebholz, Enabling accuracy of Navier-Stokes-alpha through deconvolution and enhanced stability, ESAIM: Mathematical Modelling and Numerical Analysis (M2AN), 45(2), 277-308, 2011. Download


  • M. Case, V. Ervin, A. Linke, L. Rebholz, and N. Wilson, Stable computing with an enhanced physics based scheme for the 3D Navier-Stokes equations, International Journal of Numerical Analysis and Modeling, 8(1), 118-136, 2011. Download


    • 2010


  • A. Bowers, B. Cousins, A. Linke, and L. Rebholz, New connections between finite element formulations of the Navier-Stokes equations, Journal of Computational Physics, 229, 9020-9025, 2010. Download


  • M. Case, A. Labovsky, L. Rebholz, and N. Wilson, A high physical accuracy method for incompressible magnetohydrodynamics, International Journal on Numerical Analysis and Modeling, Series B, 1(2), 219-238, 2010. Download


  • W. Miles and L. Rebholz, An enhanced physics based scheme for the NS-alpha turbulence model, Numerical Methods for Partial Differential Equations, 26, 1530-1555, 2010. Download


  • W. Layton, C.D. Pruett, and L. Rebholz, Temporally regularized direct numerical simulation, Applied Mathematics and Computation, 216, 3728-3738, 2010. Download


  • W. Layton, L. Rebholz, and M. Sussman, Energy and helicity dissipation rates of the NS-alpha and NS-alpha-deconvolution models, IMA Journal of Applied Mathematics, 75(1), 56-74, 2010. Download


  • M.A. Olshanskii and L. Rebholz, A note on helicity balance of the Galerkin method for the 3D Navier-Stokes equations, Computer Methods in Applied Mechanics and Engineering, 199, 1032-1035, 2010. Download


  • M.A. Olshanskii and L. Rebholz, Velocity-Vorticity-Helicity formulation and a solver for the Navier-Stokes equations, Journal of Computational Physics, 229(11), 4291-4303, 2010. Download


  • L. Rebholz and M. Sussman, On the high accuracy NS-alpha-deconvolution model of turbulent fluid flow, M3AS: Mathematical Models and Methods in Applied Sciences, 20(4), 611-633, 2010. Download


  • W. Layton, C. Manica, M. Neda and L. Rebholz, Numerical analysis and computational comparisons of the NS-alpha and NS-omega regularizations, Computer Methods in Applied Mechanics and Engineering, 199, 916-931, 2010. Download


    • 2009


  • L. Rebholz, Enhanced physics-based numerical schemes for two classes of turbulence models, Advances in Numerical Analysis, Volume 2009, 370289, 1-13, 2009. Download


  • W. Layton, C. Manica, M. Neda, M.A. Olshanskii and L. Rebholz, On the accuracy of the rotation form in simulations of the Navier-Stokes equations, Journal of Computational Physics, 228(9), 3433-3447, 2009. Download


  • A. Labovsky, W. Layton, C. Manica, M. Neda and L. Rebholz, The stabilized, extrapolated trapezoidal finite element method for the Navier-Stokes equations, Computer Methods in Applied Mechanics and Engineering, 198, 958-974, 2009. Download


    • 2008


  • W. Layton, C. Manica, M. Neda and L. Rebholz, Numerical Analysis and Computational Testing of a high-order Leray-deconvolution turbulence model, Numerical Methods for Partial Differential Equations, 24(2), 555-582, 2008. Download


  • L. Rebholz, A family of new high order NS-alpha models arising from helicity correction in Leray turbulence models, Journal of Mathematical Analysis and Applications, 342(1), 246-254, 2008.Download


  • W. Layton, C. Manica, M. Neda and L. Rebholz, The joint helicity-energy cascade for homogeneous, isotropic turbulence generated by approximate deconvolution models, Advances and Applications in Fluid Mechanics, 4(1), 1-46, 2008. Download


  • A. Labovschii, W. Layton, C. Manica, M. Neda, L. Rebholz, I. Stanculescu, C. Trenchea, Architecture of approximate deconvolution models of turbulence, In part I of Quality and Reliability of Large-Eddy Simulations, ERCOFTAC Series, Volume 12, editors J. Meyers, B. Guerts, P. Sagaut, 2008.


    • 2007


  • L. Rebholz, Conservation laws of turbulence models, Journal of Mathematical Analysis and Applications, 326(1), 33-45, 2007. Download


  • L. Rebholz, An Energy and Helicity conserving finite element scheme for the Navier-Stokes Equations, SIAM Journal on Numerical Analysis, 45(4), 1622-1638, 2007. Download


    • 2006

  • L. Rebholz, A multiscale V-P discretization for flow problems, Applied Mathematics and Computation, 177(1), 24-35, 2006.Download