107 citations · 459 across the 39 of their papers we have counts for
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Preconditioning of a hybridizable discontinuous Galerkin method for the coupled Stokes--Darcy system
Esteban Henríquez, Miroslav Kuchta, Jeonghun J. Lee +1
We propose parameter-robust preconditioners for the statically condensed linear system arising from a hybridizable discontinuous Galerkin discretization of the coupled Stokes--Darc…
Robust preconditioning for an HDG discretization of the time-dependent Stokes equations
Esteban Henríquez, Jeonghun J. Lee, Sander Rhebergen
We present parameter-robust preconditioners for linear systems that arise after applying static condensation to a hybridizable discontinuous Galerkin (HDG) discretization of the ti…
Preconditioning a hybridizable discontinuous Galerkin method for Navier-Stokes at high Reynolds number
Alexander D. Lindsay, Sander Rhebergen, Ben S. Southworth
We introduce a preconditioner for a hybridizable discontinuous Galerkin discretization of the linearized Navier-Stokes equations at high Reynolds number. The preconditioner is base…
Preconditioning of a hybridizable discontinuous Galerkin method for Biot's consolidation model
Esteban Henríquez, Jeonghun J. Lee, Sander Rhebergen
We present a parameter-robust preconditioner for a hybridizable discontinuous Galerkin (HDG) discretization of a four-field formulation of Biot's consolidation model. We first dete…
Parameter-robust preconditioning for hybridizable symmetric discretizations
Esteban Henriquez, Jeonghun J. Lee, Sander Rhebergen
Hybridizable discretizations allow for the elimination of local degrees-of-freedom leading to reduced linear systems. In this paper, we determine and analyse an approach to constru…
A coupled HDG/DG method for porous media with conducting/sealing faults
Aycil Cesmelioglu, Miroslav Kuchta, Jeonghun J. Lee +1
We introduce and analyze a coupled hybridizable discontinuous Galerkin/discontinuous Galerkin (HDG/DG) method for porous media in which we allow fully and partly immersed faults, a…
A posteriori error analysis of a space-time hybridizable discontinuous Galerkin method for the advection-diffusion problem
Yuan Wang, Sander Rhebergen
We present and analyze an a posteriori error estimator for a space-time hybridizable discontinuous Galerkin discretization of the time-dependent advection-diffusion problem. The re…
A hybridizable discontinuous Galerkin method for the coupled Navier-Stokes/Biot problem
Aycil Cesmelioglu, Jeonghun J. Lee, Sander Rhebergen
In this paper we present a hybridizable discontinuous Galerkin method for the time-dependent Navier-Stokes equations coupled to the quasi-static poroelasticity equations via interf…
A hybridizable discontinuous Galerkin method for the dual-porosity-Stokes problem
Aycil Cesmelioglu, Jeonghun J. Lee, Sander Rhebergen +1
We introduce and analyze a hybridizable discontinuous Galerkin (HDG) method for the dual-porosity-Stokes problem. This coupled problem describes the interaction between free flow i…
Space-time hybridizable discontinuous Galerkin method for advection-diffusion on deforming domains: The advection-dominated regime
Yuan Wang, Sander Rhebergen
We analyze a space-time hybridizable discontinuous Galerkin method to solve the time-dependent advection-diffusion equation on deforming domains. We prove stability of the discreti…
Design and analysis of an exactly divergence-free hybridized discontinuous Galerkin method for incompressible flows on meshes with quadrilateral cells
Joseph P. Dean, Sander Rhebergen, Garth N. Wells
We generalise a hybridized discontinuous Galerkin method for incompressible flow problems to non-affine cells, showing that with a suitable element mapping the generalised method p…
A strongly conservative hybridizable discontinuous Galerkin method for the coupled time-dependent Navier-Stokes and Darcy problem
A. Cesmelioglu, J. J. Lee, S. Rhebergen
We present a strongly conservative and pressure-robust hybridizable discontinuous Galerkin method for the coupled time-dependent Navier-Stokes and Darcy problem. We show existence…
A hybridizable discontinuous Galerkin method for the coupled Navier-Stokes and Darcy problem
Aycil Cesmelioglu, Sander Rhebergen
We present and analyze a strongly conservative hybridizable discontinuous Galerkin finite element method for the coupled incompressible Navier-Stokes and Darcy problem with Beavers…
Analysis of an embedded-hybridizable discontinuous Galerkin method for Biot's consolidation model
Aycil Cesmelioglu, Jeonghun J. Lee, Sander Rhebergen
We present an embedded-hybridizable discontinuous Galerkin finite element method for the total pressure formulation of the quasi-static poroelasticity model. Although the displacem…
Hybridizable discontinuous Galerkin methods for the coupled Stokes--Biot problem
Aycil Cesmelioglu, Jeonghun J. Lee, Sander Rhebergen
We present and analyze a hybridizable discontinuous Galerkin (HDG) finite element method for the coupled Stokes--Biot problem. Of particular interest is that the discrete velocitie…
A hybridizable discontinuous Galerkin method for the fully coupled time-dependent Stokes/Darcy-transport problem
Aycil Cesmelioglu, Dinh Dong Pham, Sander Rhebergen
We present a high-order hybridized discontinuous Galerkin (HDG) method for the fully coupled time-dependent Stokes-Darcy-transport problem where the fluid viscosity and source/sink…
An algebraic preconditioner for the exactly divergence-free discontinuous Galerkin method for Stokes
Sander Rhebergen, Ben S. Southworth
We present an optimal preconditioner for the exactly divergence-free discontinuous Galerkin (DG) discretization of Cockburn, Kanschat, and Schötzau [J. Sci. Comput., 31 (2007), pp.…
An interface-tracking space-time hybridizable/embedded discontinuous Galerkin method for nonlinear free-surface flows
Giselle Sosa Jones, Sander Rhebergen
We present a compatible space-time hybridizable/embedded discontinuous Galerkin discretization for nonlinear free-surface waves. We pose this problem in a two-fluid (liquid and gas…
Convergence to weak solutions of a space-time hybridized discontinuous Galerkin method for the incompressible Navier--Stokes equations
Keegan L. A. Kirk, Ayçıl Çeşmelioǧlu, Sander Rhebergen
We prove that a space-time hybridized discontinuous Galerkin method for the evolutionary Navier--Stokes equations converges to a weak solution as the time step and mesh size tend t…
Analysis of pressure-robust embedded-hybridized discontinuous Galerkin methods for the Stokes problem under minimal regularity
Aaron Baier-Reinio, Sander Rhebergen, Garth N. Wells
We present analysis of two lowest-order hybridizable discontinuous Galerkin methods for the Stokes problem, while making only minimal regularity assumptions on the exact solution.…
A conforming sliding mesh technique for an embedded-hybridized discontinuous Galerkin discretization for fluid-rigid body interaction
Tamas L. Horvath, S. Rhebergen
In (J. Comput. Phys., 417, 109577, 2020) we introduced a space-time embedded-hybridizable discontinuous Galerkin method for the solution of the incompressible Navier-Stokes equatio…
Preconditioning for a pressure-robust HDG discretization of the Stokes equations
Sander Rhebergen, Garth N. Wells
We introduce a new preconditioner for a recently developed pressure-robust hybridized discontinuous Galerkin (HDG) finite element discretization of the Stokes equations. A feature…
Analysis of an exactly mass conserving space-time hybridized discontinuous Galerkin method for the time-dependent Navier--Stokes equations
Keegan L. A. Kirk, Tamás L. Horváth, Sander Rhebergen
We introduce and analyze a space-time hybridized discontinuous Galerkin method for the evolutionary Navier--Stokes equations. Key features of the numerical scheme include point-wis…
AIR algebraic multigrid for a space-time hybridizable discontinuous Galerkin discretization of advection(-diffusion)
Abdullah A. Sivas, Ben S. Southworth, Sander Rhebergen
This paper investigates the efficiency, robustness, and scalability of approximate ideal restriction (AIR) algebraic multigrid as a preconditioner in the all-at-once solution of a…