Quadrature-Free Implementation of Discontinuous Galerkin Method for Hyperbolic Equations.

Abstract

A discontinuous Galerkin formulation that avoids the use of discrete quadrature formulas is described and applied to linear and nonlinear test problems in one and two space dimensions. This approach requires less computational time and storage than conventional implementations but preserves the compactness and robustness inherent in the discontinuous Galerkin method. Test problems include the linear and nonlinear one-dimensional scalar advection of smooth initial value problems that are discretized by using unstructured grids with varying degrees of smoothness and regularity, and two-dimensional linear Euler solutions on unstructured grids.

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Document Details

Document Type
Technical Report
Publication Date
Aug 01, 1996
Accession Number
ADA316070

Entities

People

  • Chi-Wang Shu
  • H. L. Atkins

Tags

Communities of Interest

  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Aeroacoustics
  • Boundaries
  • Computational Fluid Dynamics
  • Computational Science
  • Coordinate Systems
  • Equations
  • Euler Equations
  • Flow
  • Fluid Dynamics
  • Galerkin Method
  • Geometry
  • Integrals
  • Numbers
  • Polynomials
  • Runge Kutta Method
  • Shock Waves
  • Two Dimensional

Fields of Study

  • Mathematics

Readers

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

Technology Areas

  • Space