Accession Number : ADA293504

Title :   Adaptive Finite Element Method IV: Mesh Movement.

Descriptive Note : Final rept.

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

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

PDF Url : ADA293504

Report Date : FEB 1995

Pagination or Media Count : 37

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 error. The stability of several mesh equidistribution schemes for time dependent partial differential equations is studied. The schemes move a finite difference or finite element mesh so that a given quantity is uniform over the domain. Mesh moving methods that are based on solving a system of ordinary differential equations for the mesh velocities are considered and some of these methods are shown to be unstable with respect to an equidistributing mesh when the partial differential system is dissiptive. Simple criteria for determining the stability of a particular method are developed and the construction of stable differential systems for the mesh velocities is demonstrated. Several examples illustrating stable and unstable mesh motions are present.

Descriptors :   *FINITE ELEMENT ANALYSIS, LINEAR SYSTEMS, SPATIAL DISTRIBUTION, STABILITY, MOTION, MESH, TIME, INTEGRATION, APPROXIMATION(MATHEMATICS), BOUNDARY VALUE PROBLEMS, POLYNOMIALS, ADAPTIVE SYSTEMS, PARABOLAS, PARTIAL DIFFERENTIAL EQUATIONS, QUADRATIC EQUATIONS, VECTOR ANALYSIS.

Subject Categories : Numerical Mathematics

Distribution Statement : APPROVED FOR PUBLIC RELEASE