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We propose and rigorously analyse semi- and fully discrete discontinuous Galerkin methods for an initial and boundary value problem describing inertial viscoelasticity in terms of elastic and viscoelastic stress components, and with mixed…

Numerical Analysis · Mathematics 2023-06-27 Salim Meddahi , Ricardo Ruiz-Baier

We present a time-explicit discontinuous Galerkin (DG) solver for the time-domain acoustic wave equation on hybrid meshes containing vertex-mapped hexahedral, wedge, pyramidal and tetrahedral elements. Discretely energy-stable formulations…

Numerical Analysis · Mathematics 2016-06-22 Jesse Chan , Zheng Wang , Axel Modave , Jean-Francois Remacle , T. Warburton

The local discontinuous Galerkin (LDG) method is studied for a third-order singularly perturbed problem of the convection-diffusion type. Based on a regularity assumption for the exact solution, we prove almost $O(N^{-(k+1/2)})$ (up to a…

Numerical Analysis · Mathematics 2022-10-25 Li Yan , Zhoufeng Wang , Yao Cheng

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 elastic and viscoelastic parts in their composition. We…

Numerical Analysis · Mathematics 2020-10-19 Antonio Márquez , Salim Meddahi

We present a discontinuous Galerkin-finite-difference hybrid scheme that allows high-order shock capturing with the discontinuous Galerkin method for general relativistic magnetohydrodynamics. The hybrid method is conceptually quite simple.…

General Relativity and Quantum Cosmology · Physics 2024-01-17 Nils Deppe , François Hébert , Lawrence E. Kidder , Saul A. Teukolsky

The aim of this work is to introduce and analyze a finite element discontinuous Galerkin method on polygonal meshes for the numerical discretization of acoustic waves propagation through poroelastic materials. Wave propagation is modeled by…

Numerical Analysis · Mathematics 2021-04-14 Paola F. Antonietti , Michele Botti , Ilario Mazzieri , Simone Nati Poltri

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 formulation which immediately allows us to compute the…

Numerical Analysis · Mathematics 2023-07-06 Giselle Sosa Jones , Jeonghun J. Lee , Sander Rhebergen

We address the spatial discretization of an evolution problem arising from the coupling of viscoelastic and acoustic wave propagation phenomena by employing a discontinuous Galerkin scheme on polygonal and polyhedral meshes. The coupled…

Numerical Analysis · Mathematics 2018-12-11 Paola F. Antonietti , Francesco Bonaldi , Ilario Mazzieri

The embedded discontinuous Galerkin (EDG) method by Cockburn et al. [SIAM J. Numer. Anal., 2009, 47(4), 2686-2707] is obtained from the hybridizable discontinuous Galerkin method by changing the space of the Lagrangian multiplier from…

Numerical Analysis · Mathematics 2017-11-16 Xiao Zhang , Xiaoping Xie , Shiquan Zhang

A moving mesh discontinuous Galerkin method is presented for the numerical solution of hyperbolic conservation laws. The method is a combination of the discontinuous Galerkin method and the mesh movement strategy which is based on the…

Numerical Analysis · Mathematics 2020-04-20 Dongmi Luo , Weizhang Huang , Jianxian Qiu

We prove the inf-sup stability of a discontinuous Galerkin scheme for second order elliptic operators in (unbalanced) mesh-dependent norms for quasi-uniform meshes for all spatial dimensions. This results in a priori error bounds in these…

Numerical Analysis · Mathematics 2017-03-30 Emmanuil H. Georgoulis , Tristan Pryer

A new high order accurate semi-implicit space-time Discontinuous Galerkin method on staggered grids, for the simulation of viscous incompressible flows on two-dimensional domains is presented. The designed scheme is of the Arbitrary…

Numerical Analysis · Mathematics 2020-03-17 Francesco Lohengrin Romeo

In this paper we present an immersed weak Galerkin method for solving second-order elliptic interface problems on polygonal meshes, where the meshes do not need to be aligned with the interface. The discrete space consists of constants on…

Numerical Analysis · Mathematics 2022-08-17 Hyeokjoo Park , Do Y. Kwak

We develop a high-order hybridized discontinuous Galerkin (HDG) method for a linear degenerate elliptic equation arising from a two-phase mixture of mantle convection or glacier dynamics. We show that the proposed HDG method is well-posed…

Computational Engineering, Finance, and Science · Computer Science 2019-05-01 Shinhoo Kang , Tan Bui-Thanh , Todd Arbogast

We propose an efficient variant of a primal Discontinuous Galerkin method with interior penalty for the second order elliptic equations on very general meshes (polytopes with eventually curved boundaries). Efficiency, especially when higher…

Numerical Analysis · Mathematics 2019-03-18 Alexei Lozinski

We present and analyze a discontinuous Galerkin method for the numerical modeling of the non-linear fully-coupled thermo-hydro-mechanic problem. We propose a high-order symmetric weighted interior penalty scheme that supports general…

Numerical Analysis · Mathematics 2023-11-28 Stefano Bonetti , Michele Botti , Paola F. Antonietti

We introduce a new hybridized discontinuous Galerkin method for the incompressible magnetohydrodynamics equations. If particular velocity, pressure, magnetic field, and magnetic pressure spaces are employed for both element and trace…

Numerical Analysis · Mathematics 2022-01-07 Thad A. Gleason , Eric L. Peters , John A. Evans

We present discontinuous Galerkin (DG) methods for solving a first-order semi-linear hyperbolic system, which was originally proposed as a continuum model for a one-dimensional dimer lattice of topological resonators. We examine the…

Numerical Analysis · Mathematics 2023-05-23 Qiang Du , Huaiyu Li , Michael Weinstein , Lu Zhang

We develop a high order accurate numerical method for solving the elastic wave equation in second-order form. We hybridize the computationally efficient Cartesian grid formulation of finite differences with geometrically flexible…

Numerical Analysis · Mathematics 2025-02-04 Andreas Granath , Siyang Wang

In this paper, we propose a high-order energy-conserving semi-Lagrangian discontinuous Galerkin(ECSLDG) method for the Vlasov-Ampere system. The method employs a semi-Lagrangian discontinuous Galerkin scheme for spatial discretization of…

Numerical Analysis · Mathematics 2025-04-30 Xiaofeng Cai , Qingtao Li , Hongtao Liu , Haibiao Zheng