A Posteriori Error Estimation of Adaptive Finite Difference Schemes for Hyperbolic Systems

Abstract

We describe several techniques that are based on Richardson's extrapolation for estimating discretization errors of finite difference solutions of one- and two-dimensional hyperbolic systems. These a posteriori error estimates are intended for use with adaptive mesh moving and local refinement procedures. Mesh moving algorithms produce nonuniform grids which necessitate special treatment of solution and error estimation techniques. The required adjustments are discussed using a two-step MacCormack method as a model finite difference scheme. We also discuss automatic time step selection procedures and the effects of artificial viscosity. Extrapolation schemes that produce separate estimates of the temporal and spatial discretization errors are presented and we show how these may be used to control local mesh refinement procedures. Several examples illustrating these procedures are presented. Keywords: Hyperbolic systems, Adaptive methods, Posteriori error estimation, Finite difference methods.

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Document Details

Document Type
Technical Report
Publication Date
Jun 01, 1988
Accession Number
ADA197665

Entities

People

  • David C. Arney
  • J. E. Flaherty
  • Rupak Biswas

Organizations

  • United States Army Armament Research, Development and Engineering Center

Tags

Communities of Interest

  • C4I
  • Weapons Technologies

DTIC Thesaurus Topics

  • Algorithms
  • Applied Mathematics
  • Boundary Value Problems
  • Classification
  • Computational Science
  • Computations
  • Differential Equations
  • Engineering
  • Equations
  • Errors
  • Extrapolation
  • Fluid Dynamics
  • Mathematics
  • Military Research
  • Nonuniform
  • United States Military Academy
  • Viscosity

Fields of Study

  • Mathematics

Readers

  • Adaptive Control and Estimation with Uncertainty in Dynamic Systems.
  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)