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A new linear relaxation system for nonconservative hyperbolic systems is introduced, in which a nonlocal source term accounts for the nonconservative product of the original system. Using an asymptotic analysis the relaxation limit and its…

Numerical Analysis · Mathematics 2023-11-08 Niklas Kolbe , Michael Herty , Siegfried Müller

We present a scalable and efficient iterative solver for high-order hybridized discontinuous Galerkin (HDG) discretizations of hyperbolic partial differential equations. It is an interplay between domain decomposition methods and HDG…

Numerical Analysis · Mathematics 2016-01-29 Sriramkrishnan Muralikrishnan , Minh-Binh Tran , Tan Bui-Thanh

This paper presents a class of novel high-order fully-discrete entropy stable (ES) discontinuous Galerkin (DG) schemes with explicit time discretization. The proposed methodology exploits a critical observation from [4] that the cell…

Numerical Analysis · Mathematics 2026-03-31 Yuchang Liu , Wei Guo , Yan Jiang , Zheng Sun

In this paper, we analyze the preservation of asymptotic properties of partially dissipative hyperbolic systems when switching to a discrete setting. We prove that one of the simplest consistent and unconditionally stable numerical methods…

Analysis of PDEs · Mathematics 2024-04-17 Timothée Crin-Barat , Dragoş Manea

In this work, we present the Domain of Dependence (DoD) stabilization for systems of hyperbolic conservation laws in one space dimension. The base scheme uses a method of lines approach consisting of a discontinuous Galerkin scheme in space…

Numerical Analysis · Mathematics 2021-07-09 Sandra May , Florian Streitbürger

We consider a hybridizable discontinuous Galerkin (HDG) method for an elliptic distributed optimal control problem and we propose a balancing domain decomposition by constraints (BDDC) preconditioner to solve the discretized system. We…

Numerical Analysis · Mathematics 2025-04-04 Sijing Liu , Jinjin Zhang

Incorporation of plasmonic nanostructures in the design of photoconductive devices (PCDs) has significantly improved their optical-to-terahertz conversion efficiency. However, this improvement comes at the cost of increased complexity for…

Computational Engineering, Finance, and Science · Computer Science 2021-04-15 Liang Chen , Kostyantyn Sirenko , Ping Li , Hakan Bagci

We construct a high order discontinuous Galerkin method for solving general hyperbolic systems of conservation laws. The method is CFL-less, matrix-free, has the complexity of an explicit scheme and can be of arbitrary order in space and…

Analysis of PDEs · Mathematics 2018-02-14 David Coulette , Emmanuel Franck , Philippe Helluy , Michel Mehrenberger , Laurent Navoret

This paper is addressed to a stabilization problem of a system coupled by a wave and a Euler-Bernoulli plate equation. Only one equation is supposed to be damped. Under some assumption about the damping and the coupling terms, it is shown…

Optimization and Control · Mathematics 2018-01-03 Xiaoyu Fu , Qi Lu

In this paper, we aim to solve the system of equations governing linear elasticity in parallel using domain decomposition. Through a non-overlapping decomposition of the domain, our approach aims to target the resulting interface problem,…

Optimization and Control · Mathematics 2015-01-29 James Turner , Michal Kocvara , Daniel Loghin

An interface/boundary-unfitted eXtended hybridizable discontinuous Galerkin (X-HDG) method of arbitrary order is proposed for linear elasticity interface problems on unfitted meshes with respect to the interface and domain boundary. The…

Numerical Analysis · Mathematics 2021-02-16 Yihui Han , Xiao-Ping Wang , Xiaoping Xie

We propose a high-order hybridizable discontinuous Galerkin (HDG) formulation for the fully dynamic, linear thermo-poroelasticity problem. The governing equations are formulated as a first-order hyperbolic system incorporating solid and…

Numerical Analysis · Mathematics 2025-06-24 Salim Meddahi

In this paper we develop a staggered discontinuous Galerkin method for the Stokes and Darcy-Forchheimer problems coupled with the \Red{Beavers-Joseph-Saffman} conditions. The method is defined by imposing staggered continuity for all the…

Numerical Analysis · Mathematics 2019-06-18 Lina Zhao , Eric Chung , Eun-Jae Park , Guanyu Zhou

We propose a generalized Eulerian-Lagrangian (GEL) discontinuous Galerkin (DG) method. The method is a generalization of the Eulerian-Lagrangian (EL) DG method for transport problems proposed in [arXiv preprint arXiv: 2002.02930 (2020)],…

Numerical Analysis · Mathematics 2022-06-08 Xue Hong , Jing-Mei Qiu

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 develop subspace correction preconditioners for discontinuous Galerkin (DG) discretizations of elliptic problems with $hp$-refinement. These preconditioners are based on the decomposition of the DG finite element space…

Numerical Analysis · Mathematics 2022-11-11 Will Pazner , Tzanio Kolev

We present parameter-robust preconditioners for linear systems that arise after applying static condensation to a hybridizable discontinuous Galerkin (HDG) discretization of the time-dependent Stokes problem. Building upon the theoretical…

Numerical Analysis · Mathematics 2026-04-09 Esteban Henríquez , Jeonghun J. Lee , Sander Rhebergen

A new framework to obtain time-decay estimates for partially dissipative hyperbolic systems set on the real line is developed. Under the classical Shizuta-Kawashima (SK) stability condition, equivalent to the Kalman rank condition in…

Analysis of PDEs · Mathematics 2024-04-09 Timothée Crin-Barat , Ling-Yun Shou , Enrique Zuazua

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 formulation are established. To discretize the problem, a…

Numerical Analysis · Mathematics 2024-04-23 Salim Meddahi

We present a compatible space-time hybridizable/embedded discontinuous Galerkin discretization for nonlinear free-surface waves. We pose this problem in a two-fluid (liquid and gas) domain and use a time-dependent level-set function to…

Numerical Analysis · Mathematics 2023-07-10 Giselle Sosa Jones , Sander Rhebergen