A Local Refinement Finite Element Method for Time Dependent Partial Differential Equations.

Abstract

The authors discuss an adaptive local refinement finite element method for solving initial-boundary value problems for vector systems of partial differential equations in one space dimension and time. The method ues piecewise bilinear rectangular space-time finite elements. For each time step, grids are automatically added to regions where the local discretization error is estimated as being larger than a prescribed tolerance. The authors discuss several aspects oof their algorithm, including the tree structure that is used to represent the finite element solution and grids, an error estimation technique, and initial boundary conditions at coarse-fine mesh interfaces. The authors also present computational results for a simple linear hyperbolic problem, a problem involving Burger's equation, and a model combustion problem. Originator-supplied keywords include: Adaptive methods, Finite element methods, Local refinement, and Time dependent problems.

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Document Details

Document Type
Technical Report
Publication Date
Aug 01, 1984
Accession Number
ADA147943

Entities

People

  • J. E. Flaherty
  • P. K. Moore

Organizations

  • Rensselaer Polytechnic Institute

Tags

Communities of Interest

  • Weapons Technologies

DTIC Thesaurus Topics

  • Air Force
  • Algorithms
  • Boundaries
  • Boundary Value Problems
  • Chemical Kinetics
  • Combustion
  • Computer Science
  • Computers
  • Contracts
  • Differential Equations
  • Equations
  • Errors
  • Finite Element Analysis
  • Interpolation
  • Language
  • Lists (Data Structures)
  • Partial Differential Equations

Fields of Study

  • Mathematics

Readers

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

Technology Areas

  • Space