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Analysis of an interface stabilised finite element method for the scalar advection-diffusion-reaction equation is presented. The method inherits attractive properties of both continuous and discontinuous Galerkin methods, namely the same…

Numerical Analysis · Mathematics 2011-04-01 Garth N. Wells

In this work, we apply a time-space adaptive discontinuous Galerkin method using the elliptic reconstruction technique with a robust (in P\'eclet number) elliptic error estimator in space, for the convection dominated parabolic problems…

Numerical Analysis · Mathematics 2015-05-19 Bülent Karasözen , Murat Uzunca

In the present work, we consider weakly-singular integral equations arising from linear second-order strongly-elliptic PDE systems with constant coefficients, including, e.g., linear elasticity. We introduce a general framework for optimal…

Numerical Analysis · Mathematics 2022-04-29 Gregor Gantner , Dirk Praetorius

We propose a new discontinuous Galerkin Isogeometric Analysis (IgA) technique for the numerical solution of elliptic diffusion problems in computational domains decomposed into volumetric patches with non-matching interfaces. Due to an…

Numerical Analysis · Mathematics 2015-11-19 Christoph Hofer , Ulrich Langer , Ioannis Toulopoulos

The quasi-static multiple network poroelastic theory (MPET) model, first introduced in the context of geomechanics, has recently found new applications in medicine. In practice, the parameters in the MPET equations can vary over several…

Numerical Analysis · Mathematics 2022-05-16 Johannes Kraus , Philip L. Lederer , Maria Lymbery , Kevin Osthues , Joachim Schöberl

In this paper we present and analyse a discontinuous Galerkin finite element method (DGFEM) for the approximation of solutions to elliptic partial differential equations in nondivergence form, with oblique boundary conditions, on curved…

Numerical Analysis · Mathematics 2018-10-01 Ellya Kawecki

A discontinuous Galerkin method has been developed for strain gradient-dependent damage. The strength of this method lies in the fact that it allows the use of $C^0$ interpolation functions for continuum theories involving higher-order…

Computational Physics · Physics 2009-09-29 L. Molari , G. N. Wells , K. Garikipati , F. Ubertini

This paper proposes a matrix-free residual evaluation technique for the hybridizable discontinuous Galerkin method requiring a number of operations scaling only linearly with the number of degrees of freedom. The method results from…

Numerical Analysis · Mathematics 2020-07-24 Immo Huismann , Jörg Stiller , Jochen Fröhlich

In this paper, we develop monolithic limiting techniques for enforcing nonlinear stability constraints in enriched Galerkin (EG) discretizations of nonlinear scalar hyperbolic equations. To achieve local mass conservation and gain control…

Numerical Analysis · Mathematics 2024-12-02 Dmitri Kuzmin , Sanghyun Lee , Yi-Yung Yang

A Petrov-Galerkin finite element method is constructed for a singularly perturbed elliptic problem in two space dimensions. The solution contains a regular boundary layer and two characteristic boundary layers. Exponential splines are used…

Numerical Analysis · Mathematics 2023-11-02 Alan F. Hegarty , Eugene O'Riordan

In this paper, we propose a domain decomposition method for multiscale second order elliptic partial differential equations with highly varying coefficients. The method is based on a discontinuous Galerkin formulation. We present both a…

Numerical Analysis · Mathematics 2012-03-20 Yunfei Ma , Petter Bjorstad , Talal Rahman , Xuejun Xu

An hp-adaptive Discontinuous Galerkin Method for electromagnetic wave propagation phenomena in the time-domain is proposed. The method is highly efficient and allows for the first time the adaptive full-wave simulation of transient problems…

Computational Physics · Physics 2013-12-31 Sascha M. Schnepp

We develop a cut Discontinuous Galerkin method (cutDGM) for a diffusion-reaction equation in a bulk domain which is coupled to a corresponding equation on the boundary of the bulk domain. The bulk domain is embedded into a structured,…

Numerical Analysis · Mathematics 2017-07-10 Andre Massing

We present a new high-order accurate Lagrangian discontinuous Galerkin (DG) hydrodynamic method to simulate material dynamics (for e.g., gasses, fluids, and solids) with up to fourth-order accuracy on cubic meshes. The variables, such as…

Computational Physics · Physics 2021-03-04 Xiaodong Liu , Nathaniel R. Morgan , Evan J. Lieberman , Donald E. Burton

We consider spectral mixed discontinuous Galerkin finite element discretizations of the Lam\'e system of linear elasticity in polyhedral domains in $\mathbb{R}^3$. In order to resolve possible corner, edge, and corner-edge singularities,…

Numerical Analysis · Mathematics 2019-08-14 Thomas P. Wihler , Marcel Wirz

We formulate a numerical method for solving the two-phase flow poroelasticity equations. The scheme employs the interior penalty discontinuous Galerkin method and a sequential time-stepping method. The unknowns are the phase pressures and…

Numerical Analysis · Mathematics 2022-08-17 Boqian Shen , Beatrice Riviere

We introduce a family of discontinuous Galerkin methods to approximate the eigenvalues and eigenfunctions of a Stokes-Brinkman type of problem based in the interior penalty strategy. Under the standard assumptions on the meshes and a…

Numerical Analysis · Mathematics 2025-07-17 Felipe Lepe , Gonzalo Rivera , Jesus Vellojin

This work is concerned with the analysis of a space-time finite element discontinuous Galerkin method on polytopal meshes (XT-PolydG) for the numerical discretization of wave propagation in coupled poroelastic-elastic media. The…

Numerical Analysis · Mathematics 2023-12-05 Paola F. Antonietti , Michele Botti , Ilario Mazzieri

In this work, we study the approximation properties of multi-patch dG-IgA methods, that apply the multipatch Isogeometric Analysis (IgA) discretization concept and the discontinuous Galerkin (dG) technique on the interfaces between the…

Numerical Analysis · Mathematics 2014-08-04 Ulrich Langer , Ioannis Toulopoulos

A discontinuous Galerkin method for the ideal 5 moment two-fluid plasma system is presented. The method uses a second or third order discontinuous Galerkin spatial discretization and a third order TVD Runge-Kutta time stepping scheme. The…

Plasma Physics · Physics 2016-08-24 John Loverich , Ammar Hakim , Uri Shumlak