
Accession Number : ADA186534
Title : Adaptive Finite Element Methods for Parabolic Systems in One and TwoSpace 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 twospace dimensions. Onedimension 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. Twodimension 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