Ph.D. Mathematical Sciences, Clemson University expected 2023

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) 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..

4) 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. arxiv preprint

Sean Ingimarson

Ph.D. Mathematical Sciences, Clemson University expected 2023

Papers:

1) S. Ingimarson, An energy, momentum and angular momentum conserving scheme for a regularization model of incompressible flow,

*Journal of Numerical Mathematics*, 30(1), 1-22, 2022.

2) 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.

3) 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*, in revision.

Elizabeth Hawkins

Ph.D. Mathematical Sciences, Clemson University, expected 2025