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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

This paper presents a framework for the analysis of discretization methods based on the decomposition into local and global problems. We apply the framework to provide a comprehensive error analysis for the embedded Trefftz discontinuous…

Numerical Analysis · Mathematics 2025-12-02 Philip L. Lederer , Christoph Lehrenfeld , Paul Stocker , Igor Voulis

We present a high order time-domain nodal discontinuous Galerkin method for wave problems on hybrid meshes consisting of both wedge and tetrahedral elements. We allow for vertically mapped wedges which can be deformed along the extruded…

Numerical Analysis · Mathematics 2016-11-02 Jesse Chan , Zheng Wang , Russell J. Hewett , T. Warburton

A linear semi-implicit hybridizable discontinuous Galerkin (HDG) scheme is proposed to solve the diffusive Peterlin viscoelastic model, allowing the diffusion coefficient $\ep$ of the conformation tensor to be arbitrarily small. We…

Numerical Analysis · Mathematics 2025-03-12 Sibang Gou , Jingyan Hu , Qi Wang , Feifei Jing , Guanyu Zhou

An error analysis of a mixed discontinuous Galerkin (DG) method with Brezzi numerical flux for the time-harmonic Maxwell equations with minimal smoothness requirements is presented. The key difficulty in the error analysis for the DG method…

Numerical Analysis · Mathematics 2022-09-13 Kaifang Liu , Dietmar Gallistl , Matthias Schlottbom , J. J. W. van der Vegt

The aim of this paper is to analyze a mixed discontinuous Galerkin discretization of the time-harmonic elasticity problem. The symmetry of the Cauchy stress tensor is imposed weakly, as in the traditional dual-mixed setting. We show that…

Numerical Analysis · Mathematics 2014-10-07 Antonio Márquez , Salim Meddahi , Thanh Tran

By combining concepts from particle-in-cell (PIC) and hybridized discontinuous Galerkin (HDG) methods, we present a particle-mesh scheme which allows for diffusion-free advection, satisfies mass and momentum conservation principles in a…

Numerical Analysis · Mathematics 2018-06-27 Jakob M. Maljaars , Robert Jan Labeur , Nathaniel Trask , Deborah Sulsky

We propose a hybridizable discontinuous Galerkin (HDG) method combined with convex-concave splitting for the temporal discretization of the convective Cahn-Hilliard equation. The convection term is discretized explicitly without…

Numerical Analysis · Mathematics 2026-04-24 Gang Chen , Daozhi Han , Jiaxuan Liu , Yangwen Zhang , Dujin Zuo

In this article, a hybridizable discontinuous Galerkin (HDG) method is proposed and analyzed for the Klein-Gordon equation with local Lipschitz-type non-linearity. {\it A priori} error estimates are derived, and it is proved that…

Numerical Analysis · Mathematics 2024-11-26 Shipra Gupta , Amiya Kumar Pani , Sangita Yadav

We study higher-order space-time variational discretisations for modeling complex processes in porous media that include fluid and structure interactions which are of fundamental importance in many engineering fields with applications in…

Numerical Analysis · Mathematics 2018-05-03 Uwe Köcher , Markus Bause

We present a unified analysis for a family of variational time discretization methods, including discontinuous Galerkin methods and continuous Galerkin-Petrov methods, applied to non-stiff initial value problems. Besides the…

Numerical Analysis · Mathematics 2021-09-17 Simon Becher , Gunar Matthies

We analyze a fully discrete scheme based on the discontinuous (in time) Galerkin approach, which is combined with conforming finite element subspaces in space, for the distributed optimal control problem of the three-dimensional…

Analysis of PDEs · Mathematics 2019-06-18 Cung The Anh , Tran Minh Nguyet

This work concerns with the discontinuous Galerkin (DG)method for the time-dependent linear elasticity problem. We derive the a posteriori error bounds for semi-discrete and fully discrete problems, by making use of the stationary…

Numerical Analysis · Mathematics 2015-06-11 Thi Hong Cam Luong , Christian Daveau

In this article, we propose novel boundary treatment algorithms to avoid order reduction when implicit-explicit Runge-Kutta time discretization is used for solving convection-diffusion-reaction problems with time-dependent Di\-richlet…

Numerical Analysis · Mathematics 2024-10-07 V. González-Tabernero , J. G. López-Salas , M. J. Castro-Díaz , J. A. García-Rodríguez

In this paper we present a Local Fourier Analysis of a space-time multigrid solver for a hyperbolic test problem. The space-time discretization is based on arbitrarily high order discontinuous Galerkin spectral element methods in time and a…

Numerical Analysis · Mathematics 2021-12-07 Lea M. Versbach , Philipp Birken , Viktor Linders , Gregor Gassner

We apply the piecewise constant, discontinuous Galerkin method to discretize a fractional diffusion equation with respect to time. Using Laplace transform techniques, we show that the method is first order accurate at the \$n\$th time level…

Numerical Analysis · Mathematics 2020-03-24 William McLean , Kassem Mustapha

This paper proposes a fully discrete method called the symplectic dG full discretization for stochastic Maxwell equations driven by additive noises, based on a stochastic symplectic method in time and a discontinuous Galerkin (dG) method…

Numerical Analysis · Mathematics 2020-09-22 Chuchu Chen

This paper develops and analyses semi-discrete numerical method for two dimensional Vlasov-Stokes' system with periodic boundary condition. The method is based on coupling of semi-discrete discontinuous Galerkin method for the Vlasov…

Numerical Analysis · Mathematics 2023-12-18 Harsha Hutridurga , Krishan Kumar , Amiya K. Pani

We present an efficient nodal discontinuous Galerkin method for approximating nearly incompressible flows using the Boltzmann equations. The equations are discretized with Hermite polynomials in velocity space yielding a first order…

Numerical Analysis · Mathematics 2019-05-22 A. Karakus , N. Chalmers , J. S. Hesthaven , T. Warburton

In this paper, we use Fourier analysis to study the superconvergence of the semi-discrete discontinuous Galerkin method for scalar linear advection equations in one spatial dimension. The error bounds and asymptotic errors are derived for…

Numerical Analysis · Mathematics 2021-02-02 Sirvan Rahmati , Tianshi Lu