Accession Number : ADA186534

Title :   Adaptive Finite Element Methods for Parabolic Systems in One- and Two-Space Dimensions.

Descriptive Note : Final rept.,

Corporate Author : ARMY ARMAMENT RESEARCH, DEVELOPMENT AND ENGINEERING CENTER WATERVLIET NY BENE T WEAPONS LAB

Personal Author(s) : Adjerid, Slimane ; Flaherty, Joseph E

PDF Url : ADA186534

Report Date : Sep 1987

Pagination or Media Count : 39

Abstract : Adaptive finite element methods are given for solving initial boundary value problems for vector systems of parabolic partial differential equations in one- and two-space dimensions. One-dimension systems are discretized using piecewise linear finite element approximations in space and a backward difference code for stiff ordinary differential systems in time. A spatial error estimate is calculated using piecewise quadratic approximations that employ nodal superconvergence to increase computational efficiency. This error estimate is used to move and refine the finite element mesh in order to equidistribute a measure of the total spatial error and to satisfy a prescribed error tolerance. Ordinary differential equations for the spatial error estimate and the mesh motion are integrated in time using the same backward difference software that is used to determine the finite element solution. Two-dimension systems are discretized using piecewise bilinear finite element approximations in space and backward difference software in time. A spatial error estimate is calculated using piecewise cubic approximations that take advantage of nodal superconvergence. This error estimate is used to locally refine a stationary finite element mesh in order to satisfy a prescribed spatial error tolerance.

Descriptors :   *FINITE ELEMENT ANALYSIS, *MESH, ADAPTIVE SYSTEMS, APPROXIMATION(MATHEMATICS), BOUNDARY VALUE PROBLEMS, COMPUTATIONS, LINEARITY, ALGORITHMS, EFFICIENCY, ERRORS, PARABOLAS, PARTIAL DIFFERENTIAL EQUATIONS, SOLUTIONS(GENERAL), STATIONARY, TOLERANCE, TWO DIMENSIONAL, VECTOR ANALYSIS

Subject Categories : Numerical Mathematics

Distribution Statement : APPROVED FOR PUBLIC RELEASE