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Hybridizable Discontinuous Galerkin Methods for Thermo-Poroelastic Systems
Salim Meddahi
We propose a high-order hybridizable discontinuous Galerkin (HDG) formulation for the fully dynamic, linear thermo-poroelasticity problem. The governing equations are formulated as…
Hybridizable Discontinuous Galerkin Methods for Coupled Poro-Viscoelastic and Thermo-Viscoelastic Systems
Salim Meddahi
This article presents a unified mathematical framework for modeling coupled poro-viscoelastic and thermo-viscoelastic phenomena, formulated as a system of first-order in time parti…
An Error Analysis of HDG for Dynamic Poroelasticity
Salim Meddahi
This study introduces a hybridizable discontinuous Galerkin (HDG) method for simulating low-frequency wave propagation in poroelastic media. We present a novel four-field variation…
An Error Analysis of HDG for Linear Fluid-Structure Interaction
Salim Meddahi
A variational formulation based on velocity and stress is developed for linear fluid-structure interaction (FSI) problems. The well-posedness and energy stability of this formulati…
A DG method for a stress formulation of the elasticity eigenproblem with strongly imposed symmetry
Salim Meddahi
We introduce a pure--stress formulation of the elasticity eigenvalue problem with mixed boundary conditions. We propose an H(div)-based discontinuous Galerkin method that imposes s…
Mixed-hybrid and mixed-discontinuous Galerkin methods for linear dynamical elastic-viscoelastic composite structures
Antonio Márquez, Salim Meddahi
We introduce and analyze a stress-based formulation for Zener's model in linear viscoelasticity. The method is aimed to tackle efficiently heterogeneous materials that admit purely…