11 papers
Distributed optimal control problems governed by poroelasticity equations
Arbaz Khan, Jeonghun J. Lee, Harpal Singh
In this paper, we propose and analyze a novel two-field symmetric formulation with solid displacement and fluid pressure as main unknowns for the Biot's consolidation model in poro…
Hybridizable discontinuous Galerkin methods for poroelastic wave propagation with symmetric stress approximation
Jeonghun J. Lee, Manuel A. Sanchez
In this paper, we develop hybridized discontinuous Galerkin (HDG) methods for poroelastic wave equations. We first rewrite the governing equations to a first-order symmetric hyperb…
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…
Error Analysis of the Explicit Splitting Scheme for Fluid-Poroelastic Structure Interaction Problems
Yifan Wang, Jeonghun Lee, Suncica Canic
We present a priori error analysis for a fully discrete, parallelizable, explicit loosely coupled scheme for the time-dependent Stokes-Biot problem. The method decouples the fluid…
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 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…
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…