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In two and three dimensions, this study is focused on the numerical analysis of an eigenproblem associated with a fluid-structure model for sloshing and elasto-acoustic vibration. We use a displacement-Herrmann pressure formulation for the…

Numerical Analysis · Mathematics 2025-11-05 Arbaz Khan , Felipe Lepe , David Mora , Ricardo Ruíz-Baier , Jesus Vellojin

We study the numerical approximation by space-time finite element methods of a multi-physics system coupling hyperbolic elastodynamics with parabolic transport and modeling poro- and thermoelasticity. The equations are rewritten as a…

Numerical Analysis · Mathematics 2023-02-14 Markus Bause , Mathias Anselmann , Uwe Köcher , Florin A. Radu

This work deals with the convergence analysis of parabolic perturbations to quasilinear wave equations on smooth bounded domains. In particular, we consider wave equations with nonlinearities of quadratic type, which cover the two classical…

Analysis of PDEs · Mathematics 2021-09-29 Barbara Kaltenbacher , Vanja Nikolić

We develop and study a time-space discrete discontinuous Galerkin finite elements method to approximate the solution of one-dimensional nonlinear wave equations. We show that the numerical scheme is stable if a nonuniform time mesh is…

Analysis of PDEs · Mathematics 2021-04-07 Asma Azaiez , Mondher Benjemaa , Aida Jrajria , Hatem Zaag

This paper presents a new and unified approach to the derivation and analysis of many existing, as well as new discontinuous Galerkin methods for linear elasticity problems. The analysis is based on a unified discrete formulation for the…

Numerical Analysis · Mathematics 2021-10-12 Qingguo Hong , Jun Hu , Limin Ma , Jinchao Xu

In this paper, we present a unified analysis of the superconvergence property for a large class of mixed discontinuous Galerkin methods. This analysis applies to both the Poisson equation and linear elasticity problems with symmetric stress…

Numerical Analysis · Mathematics 2021-07-28 Limin Ma

We consider a model problem of the scattering of linear acoustic waves in free homogeneous space by an elastic solid. The stress tensor in the solid combines the effect of a linear dependence of strains with the influence of an existing…

Numerical Analysis · Mathematics 2018-04-23 Thomas S. Brown , Tonatiuh Sánchez-Vizuet , Francisco-Javier Sayas

The first super-convergent hybridisable discontinuous Galerkin (HDG) method for linear elastic problems capable of using the same degree of approximation for both the primal and mixed variables is presented. The key feature of the method is…

Numerical Analysis · Mathematics 2019-08-16 Ruben Sevilla , Matteo Giacomini , Alexandros Karkoulias , Antonio Huerta

We present and analyze a discontinuous Galerkin method for the numerical modeling of a Kelvin-Voigt thermo/poro-viscoelastic problem. We present the derivation of the model and we develop a stability analysis in the continuous setting that…

Numerical Analysis · Mathematics 2025-08-01 Stefano Bonetti , Mattia Corti

We combine continuous and discontinuous Galerkin methods in the setting of a model diffusion problem. Starting from a hybrid discontinuous formulation, we replace element interiors by more general subsets of the computational domain -…

Computational Physics · Physics 2018-11-30 Martin Vymazal , David Moxey , Chris Cantwell , Spencer Sherwin , Robert M. Kirby

Consider the scattering of a time-harmonic acoustic plane wave by a bounded elastic obstacle which is immersed in a homogeneous acoustic medium. This paper concerns an inverse acoustic-elastic interaction problem, which is to determine the…

Numerical Analysis · Mathematics 2020-04-22 Heping Dong , Jun Lai , Peijun Li

A methodology for handling block-to-block coupling of nonconforming, multiblock summation-by-parts finite difference methods is proposed. The coupling is based on the construction of projection operators that move a finite difference grid…

Numerical Analysis · Mathematics 2021-06-03 Jeremy E. Kozdon , Lucas C. Wilcox

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 derive and analyze a hybridizable discontinuous Galerkin (HDG) method for approximating weak solutions to the equations of time-harmonic linear elasticity on a bounded Lipschitz domain in three dimensions. The real symmetry of the stress…

Numerical Analysis · Mathematics 2016-11-18 Allan Hungria , Daniele Prada , Francisco-Javier Sayas

In this paper we consider Galerkin-finite element methods that approximate the solutions of initial-boundary-value problems in one space dimension for parabolic and Schr\"odinger evolution equations with dynamical boundary conditions. Error…

Numerical Analysis · Mathematics 2009-04-27 D. C. Antonopoulou , V. A. Dougalis , G. E. Zouraris

In the context of Discontinuous Galerkin methods, we study approximations of nonlinear variational problems associated with convex energies. We propose element-wise nonconforming finite element methods to discretize the continuous…

Numerical Analysis · Mathematics 2025-02-05 Georgios Grekas , Konstantinos Koumatos , Charalambos Makridakis , Andreas Vikelis

We present a computational model of thin elastic bilayers that undergo large bending isometric deformations when actuated by non-mechanical stimuli. We propose a discontinuous Galerkin approximation of the variational formulation discussed…

Numerical Analysis · Mathematics 2020-10-28 Andrea Bonito , Ricardo H. Nochetto , Dimitris Ntogkas

The problem of propagating nonlinear acoustic waves is considered; the solution to which, both with and without damping, having been obtained to-date starting from the Navier-Stokes-Duhem equations together with the continuity and thermal…

Fluid Dynamics · Physics 2021-09-29 Markus Scholle

This paper develops stable finite element pairs for the linear stress gradient elasticity model, overcoming classical elasticity's limitations in capturing size effects. We analyze mesh conditions to establish parameter-robust error…

Numerical Analysis · Mathematics 2025-08-05 Ting Lin , Shudan Tian

This work studies discontinuous Galerkin (DG) approximations of the boundary value problem for homogeneous transversely isotropic linear elastic bodies. Low-order approximations on triangles are adopted, with the use of three interior…

Analysis of PDEs · Mathematics 2019-11-26 B. J. Grieshaber , F. Rasolofoson , B. D. Reddy