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

Abstract

We 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 uses 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. We discuss several aspects of our algorithm, including the tree structure that is used to represent the finite element solution and grids, an error estimation technique, and initial and boundary conditions at coarse-fine mesh interfaces. We also present computational results for a simple linear hyperbolic problem, a problem involving Burgers' equation, and a model combustion problem.

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Document Details

Document Type
Technical Report
Publication Date
Aug 01, 1985
Accession Number
ADA159885

Entities

People

  • J. E. Flaherty
  • P. K. Moore

Organizations

  • United States Army Armament Research, Development and Engineering Center

Tags

Communities of Interest

  • Weapons Technologies

DTIC Thesaurus Topics

  • Algorithms
  • Applied Mathematics
  • Boundaries
  • Boundary Value Problems
  • Combustion
  • Computational Fluid Dynamics
  • Computational Science
  • Computer Graphics
  • Computer Science
  • Differential Equations
  • Engineering
  • Equations
  • Finite Element Analysis
  • Lists (Data Structures)
  • Mathematics
  • Military Research
  • Partial Differential Equations

Fields of Study

  • Mathematics

Readers

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

Technology Areas

  • Space