Ph.D. Mathematical Sciences, Clemson University expected 2018
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
1) L. Rebholz and M. Xiao, On reducing the splitting error in Yosida methods for the Navier-Stokes equations, Computer Methods in Appied Mechanics and Engineering,
294, 259-277 (2015). Download
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, to appear.
6) L. Rebholz, A. Viguerie and M. Xiao, Efficient nonlinear iteration schemes based on algebraic splitting for the incompressible
Navier-Stokes equations, submitted.
Ph.D. Mathematical Sciences, Clemson University expected 2019 or 2020 or thereabouts
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, submitted.
Ph.D. Mathematical Sciences, Clemson University expected 2018ish
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, submitted.