66 citations · 144 across the 22 of their papers we have counts for
26 papers · 1 filter
A Hybridizable Discontinuous Galerkin Method for Time-Modulated Drude--Lorentz Media
Jeonghun J. Lee
We formulate and analyze a hybridizable discontinuous Galerkin (HDG) method for Maxwell's equations coupled to four time-modulated Drude--Lorentz models: modulated in-coupling, mod…
Fully mixed finite element methods for the coupling of viscoelasticity and reaction-diffusion models
Alonso J. Bustos, Jeonghun J. Lee, Ricardo Ruiz-Baier
We propose and analyse a fully mixed finite element method for a two-way coupled mechanochemical model of calcium signalling in viscoelastic tissue. The mechanical response follows…
Mixed finite element methods for nonlinear reaction-diffusion equations with interfaces
Jeonghun J. Lee, Xinran Jin
We develop mixed finite element methods for nonlinear reaction-diffusion equations with interfaces which have Robin-type interface conditions. We introduce the velocity of chemical…
A posteriori error estimates of Darcy flows with Robin-type jump interface conditions
Jeonghun J. Lee
In this work we develop an a posteriori error estimator for mixed finite element methods of Darcy flow problems with Robin-type jump interface conditions. We construct an energy-no…
Coupling nonconforming and enriched Galerkin methods for robust discretization and fast solvers of poroelasticity problems
Jeonghun J. Lee, Jacob Moore
In this paper we propose a new finite element discretization for the two-field formulation of poroelasticity which uses the elastic displacement and the pore pressure as primary va…
Interior over-penalized enriched Galerkin methods for second order elliptic equations
Jeonghun J. Lee, Omar Ghattas
In this paper we propose a variant of enriched Galerkin methods for second order elliptic equations with over-penalization of interior jump terms. The bilinear form with interior o…
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 mixed method for time-transient acoustic wave propagation in metamaterials
Jeonghun J. Lee
In this paper we develop a finite element method for acoustic wave propagation in Drude-type metamaterials. The governing equation is written as a symmetrizable hyperbolic system w…
Parameter robust preconditioning by congruence for multiple-network poroelasticity
Eleonora Piersanti, Jeonghun J. Lee, Travis Thompson +2
The mechanical behaviour of a poroelastic medium permeated by multiple interacting fluid networks can be described by a system of time-dependent partial differential equations know…
Analysis of hybridized discontinuous Galerkin methods without elliptic regularity assumptions
Jeonghun J. Lee
In this paper we present new stability and optimal error analyses of hybridized discontinuous Galerkin (HDG) methods which do not require elliptic regularity assumptions. To obtain…
A hybridized discontinuous Galerkin method for Poisson-type problems with sign-changing coefficients
Jeonghun J. Lee, Sander Rhebergen
In this paper, we present a hybridized discontinuous Galerkin (HDG) method for Poisson-type problems with sign-changing coefficients. We introduce a sign-changing stabilization par…
High order approximation of Hodge Laplace problems with local coderivatives on cubical meshes
Jeonghun J. Lee
In mixed finite element approximations of Hodge Laplace problems associated with the de Rham complex, the exterior derivative operators are computed exactly, so the spatial localit…
A space-time hybridizable discontinuous Galerkin method for linear free-surface waves
Giselle Sosa Jones, Jeonghun J. Lee, Sander Rhebergen
We present and analyze a novel space-time hybridizable discontinuous Galerkin (HDG) method for the linear free-surface problem on prismatic space-time meshes. We consider a mixed f…
Unconditionally stable second order convergent partitioned methods for multiple-network poroelasticity
Jeonghun J. Lee
In this paper, we consider partitioned numerical methods for quasi-static multiple-network poroelasticity (MPET) equations, generalizations of the Biot model in poroelasticity for…
Analysis and preconditioning of parameter-robust finite element methods for Biot's consolidation model
Jeonghun J. Lee
In this paper we consider a three-field formulation of the Biot model which has the displacement, the total pressure, and the pore pressure as unknowns. For parameter-robust stabil…
A mixed finite element method for nearly incompressible multiple-network poroelasticity
Jeonghun J. Lee, Eleonora Piersanti, Kent-Andre Mardal +1
In this paper, we present and analyze a new mixed finite element formulation of a general family of quasi-static multiple-network poroelasticity (MPET) equations. The MPET equation…
Higher order multipoint flux mixed finite element methods on quadrilaterals and hexahedra
Ilona Ambartsumyan, Eldar Khattatov, Jeonghun Lee +1
We develop higher order multipoint flux mixed finite element (MFMFE) methods for solving elliptic problems on quadrilateral and hexahedral grids that reduce to cell-based pressure…
Weakly imposed symmetry and robust preconditioners for Biot's consolidation model
Trygve Baerland, Jeonghun J. Lee, Kent-Andre Mardal +1
We discuss the construction of robust preconditioners for finite element approximations of Biot's consolidation model in poroelasticity. More precisely, we study finite element met…
Analysis of an HDG Method for Linearized Incompressible Resistive MHD Equations
Jeonghun J. Lee, Stephen Shannon, Tan Bui-Thanh +1
We present a hybridized discontinuous Galerkin (HDG) method for stationary linearized incompressible magnetohydrodynamics (MHD) equations. At the heart of the paper is the introduc…
Local coderivatives and approximation of Hodge Laplace problems
Jeonghun J. Lee, Ragnar Winther
The standard mixed finite element approximations of Hodge Laplace problems associated with the de Rham complex are based on proper discrete subcomplexes. As a consequence, the exte…
Robust error analysis of coupled mixed methods for Biot's consolidation model
Jeonghun J. Lee
We study the a priori error analysis of finite element methods for Biot's consolidation model. We consider a formulation which has the stress tensor, the fluid flux, the solid disp…
Parameter-robust discretization and preconditioning of Biot's consolidation model
Jeonghun J. Lee, Kent-Andre Mardal, Ragnar Winther
Biot's consolidation model in poroelasticity has a number of applications in science, medicine, and engineering. The model depends on various parameters, and in practical applicati…
Guaranteed locking-free finite element methods for Biot's consolidation model in poroelasticity
Jeonghun J. Lee
We propose a new finite element method for the three-field formulation of Biot's consolidation model in poroelasticity and prove a priori error estimates. Uniform-in-time error est…