Books



Papers

E. Hawkins and L. Rebholz, On the choice of optimization norm for Anderson acceleration of the Picard iteration for Navier-Stokes equations, submitted. arxiv

D. Vargun, I. Monteiro and L. Rebholz, Anderson acceleration of a Picard solver for the Oldroyd-B model of viscoelastic fluids, submitted. arxiv

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, Journal of Scientific Computing, to appear, 2025. arxiv

M. Olshanskii and L. Rebholz, Approximating a branch of solutions to the Navier--Stokes equations by reduced-order modeling, Journal of Computational Physics, 524 (113728), 1-14, 2025. arxiv

A. Diegel, X. Li and L. Rebholz, Analysis of continuous data assimilation with large (or even infinite) nudging parameters, Journal of Computational and Applied Mathematics, 456 (116221), 1-16, 2025. arxiv

J. Franklin, E. Hawkins, M. Morales Hernandez and L. Rebholz, Efficiency and robustness of the (Anderson-)Picard-Newton iteration for solving nonlinear PDEs, Proceedings of the 16th World Congress in Computational Mechanics, 2024. Download

M. Dallas, S. Pollock and L. Rebholz, Analysis of an Adaptive Safeguarded Newton-Anderson Algorithm with Applications to Fluid Problems, Advances in Computational Science and Engineering, 2(3), 246-270, 2024. arxiv Journal download

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

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.

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

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

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

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.

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

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

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

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

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

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

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 .

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

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

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

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.

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

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