A multiscale V-P discretization for flow problems. - Leo G. Rebholz (Appl. Math. Comput., 2006)

An Energy- and Helicity-Conserving Finite Element Scheme for the Navier-Stokes Equations. - Leo G. Rebholz (SIAM J. Numer. Anal., 2007)

Enhanced Physics-Based Numerical Schemes for Two Classes of Turbulence Models. - Leo G. Rebholz (Adv. Numer. Anal., 2009)

On the accuracy of the rotation form in simulations of the Navier-Stokes equations. - William J. Layton; Carolina C. Manica; Monika Neda; Maxim A. Olshanskii; Leo G. Rebholz (J. Comput. Phys., 2009)

Temporally regularized direct numerical simulation. - William J. Layton; C. David Pruett; Leo G. Rebholz (Appl. Math. Comput., 2010)

New connections between finite element formulations of the Navier-Stokes equations. - Abigail L. Bowers; Benjamin R. Cousins; Alexander Linke; Leo G. Rebholz (J. Comput. Phys., 2010)

Velocity-vorticity-helicity formulation and a solver for the Navier-Stokes equations. - Maxim A. Olshanskii; Leo G. Rebholz (J. Comput. Phys., 2010)

Enforcing energy, helicity and strong mass conservation in finite element computations for incompressible Navier-Stokes simulations. - Benjamin R. Cousins; Leo G. Rebholz; Nicholas E. Wilson (Appl. Math. Comput., 2011)

On an Efficient Finite Element Method for Navier-Stokes-ω with Strong Mass Conservation. - Carolina C. Manica; Monika Neda; Maxim A. Olshanskii; Leo G. Rebholz; Nicholas E. Wilson (Comput. Methods Appl. Math., 2011)

Small-scale divergence penalization for incompressible flow problems via time relaxation. - Jeffrey M. Connors; Eleanor W. Jenkins; Leo G. Rebholz (Int. J. Comput. Math., 2011)

A Connection Between Scott-Vogelius and Grad-Div Stabilized Taylor-Hood FE Approximations of the Navier-Stokes Equations. - Michael A. Case; Vincent J. Ervin; Alexander Linke; Leo G. Rebholz (SIAM J. Numer. Anal., 2011)

On Error Analysis for the 3D Navier-Stokes Equations in Velocity-Vorticity-Helicity Form. - Hyesuk K. Lee; Maxim A. Olshanskii; Leo G. Rebholz (SIAM J. Numer. Anal., 2011)

Numerical approximation of the Voigt regularization for incompressible Navier-Stokes and magnetohydrodynamic flows. - Paul Kuberry; Adam Larios; Leo G. Rebholz; Nicholas E. Wilson (Comput. Math. Appl., 2012)

A deconvolution enhancement of the Navier-Stokes-αβ model. - Tae-Yeon Kim 001; Leo G. Rebholz; Eliot Fried (J. Comput. Phys., 2012)

A mathematical and numerical study of a filtering-based multiscale fluid model with nonlinear eddy viscosity. - Argus A. Dunca; Monika Neda; Leo G. Rebholz (Comput. Math. Appl., 2013)

Preconditioning sparse grad-div/augmented Lagrangian stabilized saddle point systems. - Sabine Le Borne; Leo G. Rebholz (Comput. Vis. Sci., 2013)

A subgrid stabilization finite element method for incompressible magnetohydrodynamics. - Mine Akbas Belenli; Songül Kaya; Leo G. Rebholz; Nicholas E. Wilson (Int. J. Comput. Math., 2013)

On the parameter choice in grad-div stabilization for the Stokes equations. - Eleanor W. Jenkins; Volker John; Alexander Linke; Leo G. Rebholz (Adv. Comput. Math., 2014)

On Crank-Nicolson Adams-Bashforth timestepping for approximate deconvolution models in two dimensions. - Songül Kaya; Carolina C. Manica; Leo G. Rebholz (Appl. Math. Comput., 2014)

Efficient, Unconditionally Stable, and Optimally Accurate FE Algorithms for Approximate Deconvolution Models. - Keith J. Galvin; Leo G. Rebholz; Catalin Trenchea (SIAM J. Numer. Anal., 2014)

Numerical Studies on a Second Order Explicitly Decoupled Variational Multiscale Method. - Mine Akbas; Songul Kaya; Leo G. Rebholz (ENUMATH, 2015)

A note on the importance of mass conservation in long-time stability of Navier-Stokes simulations using finite elements. - Mine Akbas Belenli; Leo G. Rebholz; Florentina Tone (Appl. Math. Lett., 2015)

An Explicitly Decoupled Variational Multiscale Method for Incompressible, Non-Isothermal Flows. - Mine Akbas Belenli; Songül Kaya; Leo G. Rebholz (Comput. Methods Appl. Math., 2015)

Well-posedness and a numerical study of a regularization model with adaptive nonlinear filtering for incompressible fluid flow. - Yanzhao Cao; Song Chen; Leo G. Rebholz (Comput. Math. Appl., 2016)

Sensitivity analysis of the grad-div stabilization parameter in finite element simulations of incompressible flow. - Monika Neda; Faranak Pahlevani; Leo G. Rebholz; Jiajia Waters (J. Num. Math., 2016)

An Efficient Algorithm for Computation of MHD Flow Ensembles. - Muhammad Mohebujjaman; Leo G. Rebholz (Comput. Methods Appl. Math., 2017)

High order algebraic splitting for magnetohydrodynamics simulation. - Mine Akbas; Muhammad Mohebujjaman; Leo G. Rebholz; Mengying Xiao (J. Comput. Appl. Math., 2017)

On conservation laws of Navier-Stokes Galerkin discretizations. - Sergey Charnyi; Timo Heister; Maxim A. Olshanskii; Leo G. Rebholz (J. Comput. Phys., 2017)

Energy balance and mass conservation in reduced order models of fluid flows. - Muhammad Mohebujjaman; Leo G. Rebholz; Xuping Xie; Traian Iliescu (J. Comput. Phys., 2017)

A connection between coupled and penalty projection timestepping schemes with FE spatial discretization for the Navier-Stokes equations. - Alexander Linke; Michael Neilan; Leo G. Rebholz; Nicholas E. Wilson (J. Num. Math., 2017)

Decoupled, Unconditionally Stable, Higher Order Discretizations for MHD Flow Simulation. - Timo Heister; Muhammad Mohebujjaman; Leo G. Rebholz (J. Sci. Comput., 2017)

Unconditional long-time stability of a velocity-vorticity method for the 2D Navier-Stokes equations. - Timo Heister; Maxim A. Olshanskii; Leo G. Rebholz (Numerische Mathematik, 2017)

On the Divergence Constraint in Mixed Finite Element Methods for Incompressible Flows. - Volker John; Alexander Linke; Christian Merdon; Michael Neilan; Leo G. Rebholz (SIAM Rev., 2017)

Improved Accuracy in Algebraic Splitting Methods for Navier-Stokes Equations. - Leo G. Rebholz; Mengying Xiao (SIAM J. Sci. Comput., 2017)

Data-Driven Filtered Reduced Order Modeling of Fluid Flows. - Xuping Xie; Muhammad Mohebujjaman; Leo G. Rebholz; Traian Iliescu (SIAM J. Sci. Comput., 2018)

Anderson acceleration for contractive and noncontractive operators. - Sara N. Pollock; Leo G. Rebholz (CoRR, 2019)

Pressure-induced locking in mixed methods for time-dependent (Navier-)Stokes equations. - Alexander Linke; Leo G. Rebholz (J. Comput. Phys., 2019)

POD-ROM for the Darcy-Brinkman equations with double-diffusive convection. - Fatma G. Eroglu; Songul Kaya; Leo G. Rebholz (J. Num. Math., 2019)

Efficient nonlinear iteration schemes based on algebraic splitting for the incompressible Navier-Stokes equations. - Leo G. Rebholz; Alex Viguerie; Mengying Xiao (Math. Comput., 2019)

Anderson-Accelerated Convergence of Picard Iterations for Incompressible Navier-Stokes Equations. - Sara N. Pollock; Leo G. Rebholz; Mengying Xiao (SIAM J. Numer. Anal., 2019)

Modular grad-div stabilization for multiphysics flow problems. - Mine Akbas; Leo G. Rebholz (CoRR, 2020)

Longer time accuracy for incompressible Navier-Stokes simulations with the EMAC formulation. - Maxim A. Olshanskii; Leo G. Rebholz (CoRR, 2020)

Continuous data assimilation applied to a velocity-vorticity formulation of the 2D Navier-Stokes equations. - Matthew Gardner 002; Adam Larios; Leo G. Rebholz; Duygu Vargun; Camille Zerfas (CoRR, 2020)

Analysis of Algebraic Chorin Temam splitting for incompressible NSE and comparison to Yosida methods. - Leo G. Rebholz; Alex Viguerie; Mengying Xiao (J. Comput. Appl. Math., 2020)

A Proof That Anderson Acceleration Improves the Convergence Rate in Linearly Converging Fixed-Point Methods (But Not in Those Converging Quadratically). - Claire Evans; Sara N. Pollock; Leo G. Rebholz; Mengying Xiao (SIAM J. Numer. Anal., 2020)

Modular grad-div stabilization for the incompressible non-isothermal fluid flows. - Mine Akbas; Leo G. Rebholz (Appl. Math. Comput., 2021)

Enabling fast convergence of the iterated penalty Picard iteration with $O(1)$ penalty parameter for incompressible Navier-Stokes via Anderson acceleration. - Leo G. Rebholz; Duygu Vargun; Mengying Xiao (CoRR, 2021)

Continuous data assimilation and long-time accuracy in a C0 interior penalty method for the Cahn-Hilliard equation. - Amanda E. Diegel; Leo G. Rebholz (CoRR, 2021)

An efficient algorithm for simulating ensembles of parameterized MHD flow problems. - Muhammad Mohebujjaman; Hongwei Wang; Leo G. Rebholz; Md. Abdullah Al Mahbub (CoRR, 2021)

An efficient nonlinear solver and convergence analysis for a viscoplastic flow model. - Sara N. Pollock; Leo G. Rebholz; Duygu Vargun (CoRR, 2021)

Full and Reduced Order Model Consistency of the Nonlinearity Discretization in Incompressible Flows. - Sean Ingimarson; Leo G. Rebholz; Traian Iliescu (CoRR, 2021)

Acceleration of nonlinear solvers for natural convection problems. - Sara N. Pollock; Leo G. Rebholz; Mengying Xiao (J. Num. Math., 2021)

Continuous data assimilation and long-time accuracy in a C0 interior penalty method for the Cahn-Hilliard equation. - Amanda E. Diegel; Leo G. Rebholz (Appl. Math. Comput., 2022)

An efficient algorithm for parameterized magnetohydrodynamic flow ensembles simulation. - Muhammad Mohebujjaman; Hongwei Wang; Leo G. Rebholz; Md. Abdullah Al Mahbub (Comput. Math. Appl., 2022)

Improved long time accuracy for projection methods for Navier-Stokes equations using EMAC formulation. - Sean Ingimarson; Monika Neda; Leo G. Rebholz; Jorge Reyes; An Vu (CoRR, 2022)

A mass-, kinetic energy- and helicity-conserving mimetic dual-field discretization for three-dimensional incompressible Navier-Stokes equations, part I: Periodic domains. - Yi Zhang 060; Artur Palha; Marc Gerritsma; Leo G. Rebholz (J. Comput. Phys., 2022)

Removing splitting/modeling error in projection/penalty methods for Navier-Stokes simulations with continuous data assimilation. - Elizabeth Hawkins; Leo G. Rebholz; Duygu Vargun (CoRR, 2023)

Local conservation laws of continuous Galerkin method for the incompressible Navier-Stokes equations in EMAC form. - Maxim A. Olshanskii; Leo G. Rebholz (CoRR, 2023)

Improved convergence of the Arrow-Hurwicz iteration for the Navier-Stokes equation via grad-div stabilization and Anderson acceleration. - Pelin G. Geredeli; Leo G. Rebholz; Duygu Vargun; Ahmed Zytoon (J. Comput. Appl. Math., 2023)

Long-time H1-stability of BDF2 time stepping for 2D Navier-Stokes equations. - Leo G. Rebholz; Florentina Tone (Appl. Math. Lett., 2023)

The Effect of Anderson Acceleration on Superlinear and Sublinear Convergence. - Leo G. Rebholz; Mengying Xiao (J. Sci. Comput., 2023)

Filtering for Anderson Acceleration. - Sara N. Pollock; Leo G. Rebholz (SIAM J. Sci. Comput., 2023)

Continuous data assimilation of a discretized barotropic vorticity model of geophysical flow. - Mine Akbas; Amanda E. Diegel; Leo G. Rebholz (Comput. Math. Appl., 2024)

Enhancing nonlinear solvers for the Navier-Stokes equations with continuous (noisy) data assimilation. - Bosco García-Archilla; Xuejian Li; Julia Novo; Leo G. Rebholz (CoRR, 2024)

Analysis of an Adaptive Safeguarded Newton-Anderson Algorithm with Applications to Fluid Problems. - Matt Dallas; Sara Pollock; Leo G. Rebholz (CoRR, 2024)

Analysis of continuous data assimilation with large (or even infinite) nudging parameters. - Amanda E. Diegel; Xuejian Li; Leo G. Rebholz (J. Comput. Appl. Math., 2025)

Approximating a branch of solutions to the Navier-Stokes equations by reduced-order modeling. - Maxim A. Olshanskii; Leo G. Rebholz (J. Comput. Phys., 2025)

Anderson acceleration of a Picard solver for the Oldroyd-B model of viscoelastic fluids. - Duygu Vargun; Igor O. Monteiro; Leo G. Rebholz (CoRR, 2025)

On the choice of optimization norm for Anderson acceleration of the Picard iteration for Navier-Stokes equations. - Elizabeth Hawkins; Leo G. Rebholz (CoRR, 2025)

Benchmark stress tests for flow past a cylinder at higher Reynolds numbers using EMAC. - Henry von Wahl; Leo G. Rebholz; L. Ridgway Scott (CoRR, 2025)

Analysis of the Picard-Newton Iteration for the Navier-Stokes Equations: Global Stability and Quadratic Convergence. - Sara Pollock; Leo G. Rebholz; Xuemin Tu; Mengying Xiao (J. Sci. Comput., 2025)