Unified Analysis of Discontinuous Galerkin Methods for Elliptic Problems

2002/01/01 by Douglas N. Arnold, Franco Brezzi, Bernardo Cockburn +2 · 3,262 citations
Engineering · Mathematics · #Advanced Numerical Methods in Computational Mathematics #Applied mathematics #Class (philosophy) #Computer science #Discontinuous Galerkin method #Electromagnetic Simulation and Numerical Methods #Elliptic curve #Finite element method #Galerkin method #Mathematical analysis #Mathematics #Numerical analysis #Numerical methods for differential equations #Physics

paper · doi:10.1137/s0036142901384162

published in SIAM Journal on Numerical Analysis 39(5), 1749-1779 (Society for Industrial and Applied Mathematics)

openalex publication_date 2002/01/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/04

Abstract

Abstract. We provide a framework for the analysis of a large class of discontinuous methods for second-order elliptic problems. It allows for the understanding and comparison of most of the discontinuous Galerkin methods that have been proposed over the past three decades for the numerical treatment of elliptic problems.

Citations

• An Interior Penalty Finite Element Method with Discontinuous Elements
• Mixed finite elements in ?3
• A High-Order Accurate Discontinuous Finite Element Method for the Numerical Solution of the Compressible Navier–Stokes Equations
• The Runge–Kutta Discontinuous Galerkin Method for Conservation Laws V

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