Adaptive Finite Element Method II: Error Estimation.

Abstract

An adaptive finite element method is developed to solve initial boundary value problems for vector systems of parabolic partial differential equations in one space dimension and time. The differential equations are discretized in space using piecewise linear finite element approximations. Superconvergence properties and quadratic polynomials are used to derive a computation ally inexpensive approximation to the spatial component of the error. This technique is coupled with time integration schemes of successively higher orders to obtain an approximation of the temporal and total discretization errors. Computational results indicate that these approximations converge to the exact discretization errors as the mesh is refined.

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Document Details

Document Type
Technical Report
Publication Date
Sep 01, 1994
Accession Number
ADA288358

Entities

People

  • J. E. Flaherty
  • J. M. Coyle

Organizations

  • United States Army Armament Research, Development and Engineering Center

Tags

Communities of Interest

  • Air Platforms
  • Cyber
  • Energy and Power Technologies
  • Weapons Technologies

DTIC Thesaurus Topics

  • Accuracy
  • Air Force
  • Boundaries
  • Boundary Value Problems
  • Computational Complexity
  • Computational Science
  • Decomposition
  • Difference Equations
  • Differential Equations
  • Engineering
  • Equations
  • Errors
  • Finite Element Analysis
  • Military Research
  • Partial Differential Equations
  • Polynomials
  • Security

Fields of Study

  • Mathematics

Readers

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

Technology Areas

  • Space