A Posteriori Error Estimation in a Finite Element Method for Parabolic Partial Differential Equations.

Abstract

Superconvergence properties and quadratic polynomials are used to derive a computationally inexpensive approximation to the spatial component of the error in a piecewise linear finite element method for one-dimensional parabolic partial differential equations. 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. The approximate errors are used to control an adaptive mesh refinement strategy. Keywords: Trapezoidal rule; Galerkins method.

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Document Details

Document Type
Technical Report
Publication Date
Dec 01, 1987
Accession Number
ADA190296

Entities

People

  • J. E. Flaherty
  • J. M. Coyle

Organizations

  • United States Army Armament Research, Development and Engineering Center

Tags

Communities of Interest

  • Cyber
  • Weapons Technologies

DTIC Thesaurus Topics

  • Accuracy
  • Air Force
  • Applied Mathematics
  • Classification
  • Computational Complexity
  • Differential Equations
  • Engineering
  • Equations
  • Errors
  • Finite Element Analysis
  • Information Security
  • Military Research
  • Partial Differential Equations
  • Performance Engineering
  • Polynomials
  • Schrodinger Equation
  • Security

Fields of Study

  • Mathematics

Readers

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