Adaptive Finite Element Method III: Mesh Refinement.

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 computationally 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. The approximate errors are used to control an adaptive mesh refinement strategy. Refinement is performed in space time, or both space and time depending on the dominant component of the error estimate. levels of refinement are determined automatically based on the theoretical orders of the numerical methods. Computational results provide an indication of the utility of such a strategy in keeping the total error within a prescribed tolerance.

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Document Details

Document Type
Technical Report
Publication Date
Jan 01, 1995
Accession Number
ADA293505

Entities

People

  • J. E. Flaherty
  • J. M. Coyle

Organizations

  • United States Army Armament Research, Development and Engineering Center

Tags

Communities of Interest

  • Cyber
  • Energy and Power Technologies
  • Weapons Technologies

DTIC Thesaurus Topics

  • Abstracts
  • Algorithms
  • Boundaries
  • Boundary Value Problems
  • Differential Equations
  • Engineering
  • Equations
  • Estimators
  • Finite Element Analysis
  • Galerkin Method
  • Grids
  • Information Security
  • Military Research
  • Numerical Analysis
  • Partial Differential Equations
  • Security

Fields of Study

  • Mathematics

Readers

  • Approximation Theory.
  • Linear Algebra
  • Robotics and Automation.

Technology Areas

  • Space