Adaptive Finite Element Methods for Parabolic Partial Differential Equations.

Abstract

The authors discuss a finite element method for solving initial-boundary value problems for vector systems of partial differential equations in one space dimension and time. The method automatically adjusts the computational mesh as the solution evolves in time so as to approximately minimize the local discretization error. They are thus able to calculate accurate solutions with fewer elements than would be necessary with a uniform mesh. This overall method contains two distinct steps: a solution step and a mesh selection step. They solve the partial differential equations using a finite element-Galerkin method on trapezoidal space-time-elements with either piecewise linear or cubic Hermits polynomial approximations. A variety of mesh selection strategies are discussed and analyzed. Results are presented for several computational examples.

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Document Details

Document Type
Technical Report
Publication Date
May 01, 1983
Accession Number
ADA131824

Entities

People

  • J. E. Flaherty
  • J. Michael Coyle
  • Raymond Ludwig
  • Stephen F. Davis

Organizations

  • Rensselaer Polytechnic Institute

Tags

Communities of Interest

  • Air Platforms
  • C4I
  • Energy and Power Technologies

DTIC Thesaurus Topics

  • Air Force
  • Algorithms
  • Boundary Value Problems
  • Computations
  • Differential Equations
  • Equations
  • Extrapolation
  • Finite Element Analysis
  • Galerkin Method
  • Interpolation
  • Measurement Transportation Algorithms
  • Nonlinear Algebraic Equations
  • Numerical Analysis
  • Partial Differential Equations
  • Schrodinger Equation
  • Two Dimensional
  • Wave Equations

Fields of Study

  • Mathematics

Readers

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

Technology Areas

  • Space