Accession Number : ADA288979

Title :   Adaptive Finite Element Method I: Solution Algorithm and Computational Examples.

Descriptive Note : Final rept.,

Corporate Author : ARMY ARMAMENT RESEARCH DEVELOPMENT AND ENGINEERING CENTER WATERVLIET NY BENET LABS

Personal Author(s) : Coyle, J. M. ; Flaberty, J. E.

PDF Url : ADA288979

Report Date : AUG 1994

Pagination or Media Count : 57

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. These 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. A computer code coupling this refinement strategy and stable mesh movement has been written and applied to a number of problems. These computations confirm that proper mesh movement can reduce the computational efforts associated with mesh refinement

Descriptors :   *ALGORITHMS, *FINITE ELEMENT ANALYSIS, SOFTWARE ENGINEERING, LINEAR SYSTEMS, SPATIAL DISTRIBUTION, STABILITY, ONE DIMENSIONAL, PROBLEM SOLVING, MESH, MATHEMATICAL PROGRAMMING, SOLUTIONS(GENERAL), APPROXIMATION(MATHEMATICS), NUMERICAL INTEGRATION, BOUNDARY VALUE PROBLEMS, ERRORS, POLYNOMIALS, ADAPTIVE SYSTEMS, PARTIAL DIFFERENTIAL EQUATIONS, QUADRATIC EQUATIONS, VECTOR ANALYSIS, NUMERICAL METHODS AND PROCEDURES, REFINING, FAULT TOLERANT COMPUTING.

Subject Categories : Operations Research
      Numerical Mathematics
      Computer Programming and Software

Distribution Statement : APPROVED FOR PUBLIC RELEASE