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We develop a numerical solver for three-dimensional wave propagation in coupled poroelastic-elastic media, based on a high-order discontinuous Galerkin (DG) method, with the Biot poroelastic wave equation formulated as a first order…

Computational Physics · Physics 2021-06-21 Nick Dudley Ward , Simon Eveson , Timo Lahivaara

We present a general family of subcell limiting strategies to construct robust high-order accurate nodal discontinuous Galerkin (DG) schemes. The main strategy is to construct compatible low order finite volume (FV) type discretizations…

Numerical Analysis · Mathematics 2022-11-11 Andrés M. Rueda-Ramírez , Will Pazner , Gregor J. Gassner

We consider finite element discretizations of the Biot's consolidation model in poroelasticity with MINI and stabilized P1-P1 elements. We analyze the convergence of the fully discrete model based on spatial discretization with these types…

Numerical Analysis · Mathematics 2023-07-19 Carmen Rodrigo , Francisco Gaspar , Xiaozhe Hu , Ludmil Zikatanov

In this work we propose a high-order discretization of the Baer-Nunziato two-phase flow model (Baer and Nunziato, Int. J. Multiphase Flow, 12 (1986), pp. 861-889) with closures for interface velocity and pressure adapted to the treatment of…

Numerical Analysis · Mathematics 2025-10-10 Frédéric Coquel , Claude Marmignon , Pratik Rai , Florent Renac

We develop robust solvers for a class of perturbed saddle-point problems arising in the study of a second-order elliptic equation in mixed form (in terms of flux and potential), and of the four-field formulation of Biot's consolidation…

Numerical Analysis · Mathematics 2020-11-11 Wietse M. Boon , Miroslav Kuchta , Kent-Andre Mardal , Ricardo Ruiz-Baier

Explicit time integration for immersed finite element discretizations severely suffers from the influence of poorly cut elements. In this contribution, we propose a generalized eigenvalue stabilization (GEVS) strategy for the element mass…

Computational Engineering, Finance, and Science · Computer Science 2026-01-28 Tim Bürchner , Lars Radtke , Sascha Eisenträger , Alexander Düster , Ernst Rank , Stefan Kollmannsberger , Philipp Kopp

This work presents a novel agglomeration-based multilevel preconditioner designed to accelerate the convergence of iterative solvers for linear systems arising from the discontinuous Galerkin discretization of the monodomain model in…

Numerical Analysis · Mathematics 2026-05-05 Marco Feder , Pasquale Claudio Africa

We present a method for linear stability analysis of systems with parametric uncertainty formulated in the stochastic Galerkin framework. Specifically, we assume that for a model partial differential equation, the parameter is given in the…

Numerical Analysis · Mathematics 2026-01-14 Bedřich Sousedík , Kookjin Lee

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 velocities and displacement are $H(\text{div})$-conforming and…

Numerical Analysis · Mathematics 2023-07-07 Aycil Cesmelioglu , Jeonghun J. Lee , Sander Rhebergen

The robust, scalable simulation of flowing electrochemical systems is increasingly important due to the synergy between intermittent renewable energy and electrochemical technologies such as energy storage and chemical manufacturing. The…

Numerical Analysis · Mathematics 2022-12-21 Thomas Roy , Julian Andrej , Victor A. Beck

We present families of space-time finite element methods (STFEMs) for a coupled hyperbolic-parabolic system of poro- or thermoelasticity. Well-posedness of the discrete problems is proved. Higher order approximations inheriting most of the…

Numerical Analysis · Mathematics 2023-03-14 Mathias Anselmann , Markus Bause , Nils Margenberg , Pavel Shamko

We study the numerical approximation of a coupled hyperbolic-parabolic system by a family of discontinuous Galerkin space-time finite element methods. The model is rewritten as a first-order evolutionary problem that is treated by the…

Numerical Analysis · Mathematics 2024-06-21 Markus Bause , Sebastian Franz

In this work we analyze an optimized artificial fixed-stress iteration scheme for the numerical approximation of the Biot system modelling fluid flow in deformable porous media. The iteration is based on a prescribed constant artificial…

Numerical Analysis · Mathematics 2017-05-24 M. Bause , F. A. Radu , U. Köcher

In this paper we propose and analyze a staggered discontinuous Galerkin method for a five-field formulation of the Biot system of poroelasticity on general polygonal meshes. Elasticity is equipped with stress-displacement-rotation…

Numerical Analysis · Mathematics 2020-11-11 Lina Zhao , Eric Chung , Eun-Jae Park

An inherent regularization strategy and block Schur complement preconditioning are studied for linear poroelasticity problems discretized using the lowest-order weak Galerkin FEM in space and the implicit Euler scheme in time. At each time…

Numerical Analysis · Mathematics 2025-07-31 Weizhang Huang , Zhuoran Wang

We equip a high-order continuous Galerkin discretization of a general hyperbolic problem with a nonlinear stabilization term and introduce a new methodology for enforcing preservation of invariant domains. The amount of shock-capturing…

Numerical Analysis · Mathematics 2026-02-17 Dmitri Kuzmin , Hennes Hajduk , Joshua Vedral

We implement a stabilized finite element method for steady Darcy-Brinkman-Forchheimer model within the continuous Galerkin framework. The nonlinear fluid model is first linearized using a standard \textit{Newton's method. The sequence of…

Numerical Analysis · Mathematics 2025-01-09 Hyun Chul Yoon , S. M. Mallikarjunaiah

We formulate and analyze interior penalty discontinuous Galerkin methods for coupled elliptic PDEs modeling excitable tissue, represented by intracellular and extracellular domains sharing a common interface. The PDEs are coupled through a…

Numerical Analysis · Mathematics 2024-11-06 Rami Masri , Keegan L. A. Kirk , Eirill Hauge , Miroslav Kuchta

The high-order accurate continuous Galerkin finite element method offers attractive computational efficiency for computational fluid dynamics. A challenge is however spurious oscillations which result for convection dominated flows over…

Numerical Analysis · Mathematics 2023-11-10 Arnaud G. Malan , Jan Nordstrom

We propose parameter-robust preconditioners for the statically condensed linear system arising from a hybridizable discontinuous Galerkin discretization of the coupled Stokes--Darcy system. The design strategy relies on first applying the…

Numerical Analysis · Mathematics 2026-04-27 Esteban Henríquez , Miroslav Kuchta , Jeonghun J. Lee , Sander Rhebergen