The Local Discontinuous Galerkin Method for Time-Dependent Convection-Diffusion Systems.

Abstract

In this paper, we study the Local Discontinuous Galerkin methods for non-linear, time-dependent convection-diffusion systems. These methods are an extension of the Runge-Kutta Discontinuous Galerkin methods for purely hyperbolic systems to convection-diffusion systems and share with those methods their high parallelizability, their high-order formal accuracy, and their easy handling of complicated geometries, for convection dominated problems. It is proven that for scalar equations, the Local Discontinuous Galerkin methods are L2-stable in the nonlinear case. Moreover, in the linear case, it is shown that if polynomials of degree k are used, the methods are k-th order accurate for general triangulations; although this order of convergence is suboptimal, it is sharp for the LDG methods. Preliminary numerical examples displaying the performance of the method are shown.

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Document Details

Document Type
Technical Report
Publication Date
Jul 01, 1997
Accession Number
ADA329509

Entities

People

  • Bernardo Cockburn
  • Chi-Wang Shu

Tags

Communities of Interest

  • Biomedical

DTIC Thesaurus Topics

  • Commerce
  • Computational Fluid Dynamics
  • Computational Science
  • Convection
  • Education
  • Electronic Mail
  • Equations
  • Galerkin Method
  • Geometry
  • Health Care
  • Inequalities
  • Law
  • Materials
  • Navier Stokes Equations
  • Polynomials
  • Public Policy
  • Two Dimensional

Fields of Study

  • Mathematics

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  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)