Leo G. Rebholz

Publication Activity (10 Years)

Years Active: 2006-2024
Publications (10 Years): 46

Top Topics

Finite Element Methods

Navier Stokes Equations

Top Venues

J. Comput. Phys.

SIAM J. Numer. Anal.

Publications

Matt Dallas, Sara Pollock, Leo G. Rebholz
Analysis of an Adaptive Safeguarded Newton-Anderson Algorithm with Applications to Fluid Problems. CoRR (2024)
Mine Akbas, Amanda E. Diegel, Leo G. Rebholz
Continuous data assimilation of a discretized barotropic vorticity model of geophysical flow. Comput. Math. Appl. 160 (2024)
Sara Pollock, Leo G. Rebholz, Xuemin Tu, Mengying Xiao
Analysis of the Picard-Newton iteration for the Navier-Stokes equations: global stability and quadratic convergence. CoRR (2024)
Leo G. Rebholz, Florentina Tone
Long-time H1-stability of BDF2 time stepping for 2D Navier-Stokes equations. Appl. Math. Lett. 141 (2023)
Sara N. Pollock, Leo G. Rebholz
Filtering for Anderson Acceleration. SIAM J. Sci. Comput. 45 (4) (2023)
Elizabeth Hawkins, Leo G. Rebholz, Duygu Vargun
Removing splitting/modeling error in projection/penalty methods for Navier-Stokes simulations with continuous data assimilation. CoRR (2023)
Pelin G. Geredeli, Leo G. Rebholz, Duygu Vargun, Ahmed Zytoon
Improved convergence of the Arrow-Hurwicz iteration for the Navier-Stokes equation via grad-div stabilization and Anderson acceleration. J. Comput. Appl. Math. 422 (2023)
Leo G. Rebholz, Mengying Xiao
The Effect of Anderson Acceleration on Superlinear and Sublinear Convergence. J. Sci. Comput. 96 (2) (2023)
Maxim A. Olshanskii, Leo G. Rebholz
Local conservation laws of continuous Galerkin method for the incompressible Navier-Stokes equations in EMAC form. CoRR (2023)
Pelin G. Geredeli, Leo G. Rebholz, Duygu Vargun, Ahmed Zytoon
Improved convergence of the Arrow-Hurwicz iteration for the Navier-Stokes equation via grad-div stabilization and Anderson acceleration. CoRR (2022)
Muhammad Mohebujjaman, Hongwei Wang, Leo G. Rebholz, Md. Abdullah Al Mahbub
An efficient algorithm for parameterized magnetohydrodynamic flow ensembles simulation. Comput. Math. Appl. 112 (2022)
Amanda E. Diegel, Leo G. Rebholz
Continuous data assimilation and long-time accuracy in a C0 interior penalty method for the Cahn-Hilliard equation. Appl. Math. Comput. 424 (2022)
Sean Ingimarson, Monika Neda, Leo G. Rebholz, Jorge Reyes, An Vu
Improved long time accuracy for projection methods for Navier-Stokes equations using EMAC formulation. CoRR (2022)
Sara N. Pollock, Leo G. Rebholz
Filtering for Anderson acceleration. CoRR (2022)
Yi Zhang, Artur Palha, Marc Gerritsma, Leo G. Rebholz
A mass-, kinetic energy- and helicity-conserving mimetic dual-field discretization for three-dimensional incompressible Navier-Stokes equations, part I: Periodic domains. J. Comput. Phys. 451 (2022)
Leo G. Rebholz, Duygu Vargun, Mengying Xiao
Enabling fast convergence of the iterated penalty Picard iteration with $O(1)$ penalty parameter for incompressible Navier-Stokes via Anderson acceleration. CoRR (2021)
Sara N. Pollock, Leo G. Rebholz, Mengying Xiao
Acceleration of nonlinear solvers for natural convection problems. J. Num. Math. 29 (4) (2021)
Yi Zhang, Artur Palha, Marc Gerritsma, Leo G. Rebholz
A mass-, kinetic energy- and helicity-conserving mimetic dual-field discretization for three-dimensional incompressible Navier-Stokes equations, part I: Periodic domains. CoRR (2021)
Amanda E. Diegel, Leo G. Rebholz
interior penalty method for the Cahn-Hilliard equation. CoRR (2021)
Sara N. Pollock, Leo G. Rebholz, Duygu Vargun
An efficient nonlinear solver and convergence analysis for a viscoplastic flow model. CoRR (2021)
Muhammad Mohebujjaman, Hongwei Wang, Leo G. Rebholz, Md. Abdullah Al Mahbub
An efficient algorithm for simulating ensembles of parameterized MHD flow problems. CoRR (2021)
Mine Akbas, Leo G. Rebholz
Modular grad-div stabilization for the incompressible non-isothermal fluid flows. Appl. Math. Comput. 393 (2021)
Sean Ingimarson, Leo G. Rebholz, Traian Iliescu
Full and Reduced Order Model Consistency of the Nonlinearity Discretization in Incompressible Flows. CoRR (2021)
Mine Akbas, Leo G. Rebholz
Modular grad-div stabilization for multiphysics flow problems. CoRR (2020)
Leo G. Rebholz, Alex Viguerie, Mengying Xiao
Analysis of Algebraic Chorin Temam splitting for incompressible NSE and comparison to Yosida methods. J. Comput. Appl. Math. 365 (2020)
Claire Evans, Sara N. Pollock, Leo G. Rebholz, Mengying Xiao
A Proof That Anderson Acceleration Improves the Convergence Rate in Linearly Converging Fixed-Point Methods (But Not in Those Converging Quadratically). SIAM J. Numer. Anal. 58 (1) (2020)
Matthew Gardner, Adam Larios, Leo G. Rebholz, Duygu Vargun, Camille Zerfas
Continuous data assimilation applied to a velocity-vorticity formulation of the 2D Navier-Stokes equations. CoRR (2020)
Sara N. Pollock, Leo G. Rebholz, Mengying Xiao
Acceleration of nonlinear solvers for natural convection problems. CoRR (2020)
Maxim A. Olshanskii, Leo G. Rebholz
Longer time accuracy for incompressible Navier-Stokes simulations with the EMAC formulation. CoRR (2020)
Fatma G. Eroglu, Songul Kaya, Leo G. Rebholz
POD-ROM for the Darcy-Brinkman equations with double-diffusive convection. J. Num. Math. 27 (3) (2019)
Sara N. Pollock, Leo G. Rebholz, Mengying Xiao
Anderson-Accelerated Convergence of Picard Iterations for Incompressible Navier-Stokes Equations. SIAM J. Numer. Anal. 57 (2) (2019)
Sara N. Pollock, Leo G. Rebholz
Anderson acceleration for contractive and noncontractive operators. CoRR (2019)
Alexander Linke, Leo G. Rebholz
Pressure-induced locking in mixed methods for time-dependent (Navier-)Stokes equations. J. Comput. Phys. 388 (2019)
Leo G. Rebholz, Alex Viguerie, Mengying Xiao
Efficient nonlinear iteration schemes based on algebraic splitting for the incompressible Navier-Stokes equations. Math. Comput. 88 (318) (2019)
Xuping Xie, Muhammad Mohebujjaman, Leo G. Rebholz, Traian Iliescu
Data-Driven Filtered Reduced Order Modeling of Fluid Flows. SIAM J. Sci. Comput. 40 (3) (2018)
Leo G. Rebholz, Mengying Xiao
Improved Accuracy in Algebraic Splitting Methods for Navier-Stokes Equations. SIAM J. Sci. Comput. 39 (4) (2017)
Timo Heister, Muhammad Mohebujjaman, Leo G. Rebholz
Decoupled, Unconditionally Stable, Higher Order Discretizations for MHD Flow Simulation. J. Sci. Comput. 71 (1) (2017)
Alexander Linke, Michael Neilan, Leo G. Rebholz, Nicholas E. Wilson
A connection between coupled and penalty projection timestepping schemes with FE spatial discretization for the Navier-Stokes equations. J. Num. Math. 25 (4) (2017)
Volker John, Alexander Linke, Christian Merdon, Michael Neilan, Leo G. Rebholz
On the Divergence Constraint in Mixed Finite Element Methods for Incompressible Flows. SIAM Rev. 59 (3) (2017)
Mine Akbas, Muhammad Mohebujjaman, Leo G. Rebholz, Mengying Xiao
High order algebraic splitting for magnetohydrodynamics simulation. J. Comput. Appl. Math. 321 (2017)
Muhammad Mohebujjaman, Leo G. Rebholz, Xuping Xie, Traian Iliescu
Energy balance and mass conservation in reduced order models of fluid flows. J. Comput. Phys. 346 (2017)
Sergey Charnyi, Timo Heister, Maxim A. Olshanskii, Leo G. Rebholz
On conservation laws of Navier-Stokes Galerkin discretizations. J. Comput. Phys. 337 (2017)
Timo Heister, Maxim A. Olshanskii, Leo G. Rebholz
Unconditional long-time stability of a velocity-vorticity method for the 2D Navier-Stokes equations. Numerische Mathematik 135 (1) (2017)
Muhammad Mohebujjaman, Leo G. Rebholz
An Efficient Algorithm for Computation of MHD Flow Ensembles. Comput. Methods Appl. Math. 17 (1) (2017)
Yanzhao Cao, Song Chen, Leo G. Rebholz
Well-posedness and a numerical study of a regularization model with adaptive nonlinear filtering for incompressible fluid flow. Comput. Math. Appl. 71 (11) (2016)
Monika Neda, Faranak Pahlevani, Leo G. Rebholz, Jiajia Waters
Sensitivity analysis of the grad-div stabilization parameter in finite element simulations of incompressible flow. J. Num. Math. 24 (3) (2016)
Mine Akbas Belenli, Leo G. Rebholz, Florentina Tone
A note on the importance of mass conservation in long-time stability of Navier-Stokes simulations using finite elements. Appl. Math. Lett. 45 (2015)
Mine Akbas Belenli, Songül Kaya, Leo G. Rebholz
An Explicitly Decoupled Variational Multiscale Method for Incompressible, Non-Isothermal Flows. Comput. Methods Appl. Math. 15 (1) (2015)
Mine Akbas, Songul Kaya, Leo G. Rebholz
Numerical Studies on a Second Order Explicitly Decoupled Variational Multiscale Method. ENUMATH (2015)
Songül Kaya, Carolina C. Manica, Leo G. Rebholz
On Crank-Nicolson Adams-Bashforth timestepping for approximate deconvolution models in two dimensions. Appl. Math. Comput. 246 (2014)
Eleanor W. Jenkins, Volker John, Alexander Linke, Leo G. Rebholz
On the parameter choice in grad-div stabilization for the Stokes equations. Adv. Comput. Math. 40 (2) (2014)
Keith J. Galvin, Leo G. Rebholz, Catalin Trenchea
Efficient, Unconditionally Stable, and Optimally Accurate FE Algorithms for Approximate Deconvolution Models. SIAM J. Numer. Anal. 52 (2) (2014)
Argus A. Dunca, Monika Neda, Leo G. Rebholz
A mathematical and numerical study of a filtering-based multiscale fluid model with nonlinear eddy viscosity. Comput. Math. Appl. 66 (6) (2013)
Mine Akbas Belenli, Songül Kaya, Leo G. Rebholz, Nicholas E. Wilson
A subgrid stabilization finite element method for incompressible magnetohydrodynamics. Int. J. Comput. Math. 90 (7) (2013)
Sabine Le Borne, Leo G. Rebholz
Preconditioning sparse grad-div/augmented Lagrangian stabilized saddle point systems. Comput. Vis. Sci. 16 (6) (2013)
Tae-Yeon Kim, Leo G. Rebholz, Eliot Fried
A deconvolution enhancement of the Navier-Stokes-αβ model. J. Comput. Phys. 231 (11) (2012)
Paul Kuberry, Adam Larios, Leo G. Rebholz, Nicholas E. Wilson
Numerical approximation of the Voigt regularization for incompressible Navier-Stokes and magnetohydrodynamic flows. Comput. Math. Appl. 64 (8) (2012)
Hyesuk K. Lee, Maxim A. Olshanskii, Leo G. Rebholz
On Error Analysis for the 3D Navier-Stokes Equations in Velocity-Vorticity-Helicity Form. SIAM J. Numer. Anal. 49 (2) (2011)
Benjamin R. Cousins, Leo G. Rebholz, Nicholas E. Wilson
Enforcing energy, helicity and strong mass conservation in finite element computations for incompressible Navier-Stokes simulations. Appl. Math. Comput. 218 (4) (2011)
Carolina C. Manica, Monika Neda, Maxim A. Olshanskii, Leo G. Rebholz, Nicholas E. Wilson
On an Efficient Finite Element Method for Navier-Stokes-ω with Strong Mass Conservation. Comput. Methods Appl. Math. 11 (1) (2011)
Michael A. Case, Vincent J. Ervin, Alexander Linke, Leo G. Rebholz
A Connection Between Scott-Vogelius and Grad-Div Stabilized Taylor-Hood FE Approximations of the Navier-Stokes Equations. SIAM J. Numer. Anal. 49 (4) (2011)
Jeffrey M. Connors, Eleanor W. Jenkins, Leo G. Rebholz
Small-scale divergence penalization for incompressible flow problems via time relaxation. Int. J. Comput. Math. 88 (15) (2011)
William J. Layton, C. David Pruett, Leo G. Rebholz
Temporally regularized direct numerical simulation. Appl. Math. Comput. 216 (12) (2010)
Abigail L. Bowers, Benjamin R. Cousins, Alexander Linke, Leo G. Rebholz
New connections between finite element formulations of the Navier-Stokes equations. J. Comput. Phys. 229 (24) (2010)
Maxim A. Olshanskii, Leo G. Rebholz
Velocity-vorticity-helicity formulation and a solver for the Navier-Stokes equations. J. Comput. Phys. 229 (11) (2010)
William J. Layton, Carolina C. Manica, Monika Neda, Maxim A. Olshanskii, Leo G. Rebholz
On the accuracy of the rotation form in simulations of the Navier-Stokes equations. J. Comput. Phys. 228 (9) (2009)
Leo G. Rebholz
Enhanced Physics-Based Numerical Schemes for Two Classes of Turbulence Models. Adv. Numer. Anal. 2009 (2009)
Leo G. Rebholz
An Energy- and Helicity-Conserving Finite Element Scheme for the Navier-Stokes Equations. SIAM J. Numer. Anal. 45 (4) (2007)
Leo G. Rebholz
A multiscale V-P discretization for flow problems. Appl. Math. Comput. 177 (1) (2006)