**Duygu Vargun**Ph.D. 2023 (expected)

September 2023 -, Postdoc, Oak Ridge National Lab

**Awards:**

Michael Case Award for Outstanding Promise in Applied/Computational Mathematics, 2021

**Papers:**

1) 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

2) 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

3) 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*, to appear.

4) 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.

**Camille Zerfas**Ph.D. 2019

August 2019- , Data Scientist, NextEra Energy

**Awards:**

College of Science Outstanding Graduate in Teaching, 2019

Outstanding Graduate in Teaching, School of Mathematical and Statistical Sciences, 2019

Michael Case Award for Outstanding Promise in Applied/Computational Mathematics, 2017

**Papers:**

1) 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.

2) M. Akbas, L. Rebholz and C. Zerfas, Optimal vorticity accuracy in an efficient velocity-vorticity method for the 2D Navier-Stokes equations,

*Calcolo*, 55(1):3, 1-29, 2018.

3) L. Rebholz, D. Wang, Z. Wang, K. Zhao, and C. Zerfas, Initial boundary value problems for a system of parabolic conservation laws arising from a Keller-Segel type chemotaxis model in multiple space dimensions,

*DCDS-A*, 39(7), 3789-3838, 2019.

4) 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.

5) L. Rebholz and C. Zerfas, Simple and efficient continuous data assimilation of evolution equations via algebraic nudging, submitted. Arxiv preprint

6) C. Zerfas, L. Rebholz, M. Schneier and T. Iliescu, Continuous data assimilation reduced order models of fluid flow, submitted. arxiv

**Mengying Xiao**Ph.D. 2018 (co-advisor Timo Heister)

2020-, (tenure track) Assistant Professor, University of West Florida

2019-2020, Postdoc, University of Florida

2018-2019, Visiting Assitant Professor, William & Mary

**Awards (while a student):**

College of Science Outstanding Graduate in Discovery, 2018

Most Outstanding Graduate Student Researcher award, Department of Mathematical Sciences, 2018

Outstanding Graduate Student Researcher award, Department of Mathematical Sciences, 2017

Outstanding TA award, Department of Mathematical Sciences, 2016

Michael Case award for Outstanding Promise in Applied/Computational Mathematics, 2014

**Papers:**(while a student)

1) L. Rebholz and M. Xiao, On reducing the splitting error in Yosida methods for the Navier-Stokes equations,

*Computer Methods in Applied Mechanics and Engineering*, 294, 259-277, 2015.

2) 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.

3) L. Rebholz and M. Xiao, Improved accuracy in algebraic splitting methods for \ Navier-Stokes equations,

*SIAM Journal of Scientific Computing*, 39(4), A1489-A1513, 2017.

4) 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.

5) 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 of Numerical Analysis and Modeling*, 15(4), 649-676, 2018.

6) L. Rebholz, A. Viguerie and M. Xiao, Efficient nonlinear iteration schemes based on algebraic splitting for the incompressible Navier-Stokes equations,

*Mathematics of Computation*, to appear.

**Sergey Charnyi**Ph.D. 2018 (co-advisor Timo Heister)

2021-, Staff Scientist, Siemens

2019-2021, Postdoc, Naval Postgraduate School

**Papers:**(while a student)

1) 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.

2) S. Charnyi, T. Heister, M. Olshanskii and L. Rebholz, Efficient discretizations for the EMAC formulation of the incompressible Navier-Stokes equations,

*Applied Numerical Mathematics*, to appear.

**Muhammad Mohebujjaman**Ph.D. 2017 (co-advisor Timo Heister)

2020-, (tenure track) Assistant Professor, Texas A&M International University

2019-2020, Postdoc, MIT

2017-January 2019 , Postdoc, Virginia Tech

**Papers**(while a student):

1) 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.

2) N. Jiang, M. Mohebujjaman, L. Rebholz and C. Trenchea, Analysis of a family of optima$

*Computer Methods in Applied Mechanics and Engineering*, 310, 388-405, 2016.

3) T. Heister, M. Mohebujjaman and L. Rebholz, Decoupled, unconditionally stable, higher$ for MHD flow simulation,

*Journal of Scientific Computing*, 71(1), 21-43, 2017.

4) M. Mohebujjaman and L. Rebholz, An efficient algorithm for computation of MHD flow en$

*Computational Methods in Applied Mathematics*, 17(1), 121-137, 2017.

5) 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.

**Mine Akbas**, Ph.D. 2016 (co-advisor Songul Kaya at Middle East Technical University)

2018-, Assistant Professor, Duzce University (Turkey)

2016-2018 , Postdoc, Duzce University

**Papers**(while a student):

1) M. Akbas 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.

2) M. Akbas 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.

3) M. Akbas Belenli, L. Rebholz, and F. Tone, A note on the importance of mass conservation in long-time stability of Navier-Stokes equations

*Applied Mathematics Letters*, 45, 98-102, 2015.

4) M. Akbas Belenli, 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.

5) M. Akbas Belenli, S. Kaya and L. Rebholz, On the stability at all times of linearly extrapolated BDF2 timestepping for multiphysics incompressib$ flow problems,

*Numerical Methods for Partial Differential Equations*, 33(4), 995-1017, 2017.

**Abigail Bowers**, Ph.D. 2014

2016- , Assistant Professor, Florida Polytechnic University

2014-2016 , Visiting Assistant Professor, Clemson

**Papers**(while a student):

7) 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.

6) 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.

5) A. Bowers, Numerical approximation of a multiscale Leray model for incompressible, viscous flow, 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.

4) 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.

3) 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.

2) 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.

1) 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(24), 2090-2095, 2010.

**Keith Galvin**, Ph.D. 2013 (co-advised by Hyesuk Lee)

August 2013-May 2014, Postdoc, University of Michigan

May 2014 - present, Mathematician, Applied Physical Sciences

Papers while a student:

1)

**K. Galvin**, New subgrid artificial viscosity methods for the Navier-Stokes equations,

*Computer Methods in Applied Mechanics and Engineering*, 200(1-4), 242-250, 2011. Download

2)

**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

3)

**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

4)

**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

5) K. Galvin and H.K. Lee, Analysis and approximation of the Cross model for quasi-Newtonian flows with defective boundary conditions,

*Appl. Math. and Compt.*, 222, 244-254, 2013.

6) K. Galvin, L. Rebholz, and C. Trenchea, Efficient, unconditionally stable, and optimally accurate FE algorithms for approximate deconvolution models,

*SIAM Journal on Numerical Analysis*, to appear.

Awards during time at Clemson:

(Most) Outstanding PhD Student award, Clemson University Dept of Mathematical Sciences, 2012

Voted worst golfer in computational math golf group, 2011-2013.

**Nicholas Wilson**, Ph.D. 2012

August 2012-May 2013: Visiting Assistant Professor, Michigan Tech

May 2013-present: Risk Analyst, Disney

Publications during time at Clemson:

1) M. Case, A. Labovsky, L. Rebholz, and

**N. Wilson**, A high physical accuracy method for incompressible magnetohydrodynamics,

*International Journal of Numerical Analysis and Modeling, Series B*, 1(2), 219-238, 2010.

2) 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*, 218, 1208-1221, 2011.

3) 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.

4) C. Manica, M. Neda, M. 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.

5) 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.

6)

**N. Wilson**, On the Leray-deconvolution model for the incompressible Magnetohydrodynamics equations,

*Applied Mathematics and Computation*, 218(21), 10557-10571, 2012.

7) 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.

8) P. Kuberry, A. Larios, L. Rebholz, and

**N. Wilson**, Numerical approximation of the Voigt regularization of incompressible NSE and MHD flows,

*Computers and Mathematics with Applications*, 64(8), 2647-2662, 2012.

9) M. Belenli, S. Kaya, L. Rebholz, and

**N. Wilson**, A subgrid stabilization finite element method for incompresible magnetohydrodynamics,

*International Journal of Computer Mathematics*, 90(7), 1506-1523, 2013..

Awards during time at Clemson:

(Most) Outstanding PhD Student award, Clemson University Dept of Mathematical Sciences, 2011.

Clayton & Claire Aucoin Enhancement Award (Travel money award for PhD students with outstanding potential to be leaders in research), 2011.

**Michael Case**, Ph.D. 2010 (co-advised by Lea Jenkins)

Publications during time at Clemson:

1)

**M. Case**, A. Labovsky, L. Rebholz, and N. Wilson, A high physical accuracy method for incompressible magnetohydrodynamics,

*International Journal of Numerical Analysis and Modeling, Series B*, 1(2), 219-238, 2010. Download

2)

**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

3)

**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

4)

**M. Case**and H. MacMillan, On simulating the generation of mosaicism furing mammalian cerebral cortical development,

*Journal of Biological Systems*, 17(1), 27-62, 2009. Download

Awards during time at Clemson:

SIAM Southeast Student Paper Prize, April 2010