Accession Number : ADA293505

Title :   Adaptive Finite Element Method III: Mesh Refinement.

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 : ADA293505

Report Date : JAN 1995

Pagination or Media Count : 25

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.

Descriptors :   *FINITE ELEMENT ANALYSIS, LINEAR SYSTEMS, SPATIAL DISTRIBUTION, COMPUTATIONS, MESH, ESTIMATES, INTEGRATION, APPROXIMATION(MATHEMATICS), BOUNDARY VALUE PROBLEMS, ERRORS, POLYNOMIALS, ADAPTIVE SYSTEMS, PARABOLAS, PARTIAL DIFFERENTIAL EQUATIONS, QUADRATIC EQUATIONS, VECTOR ANALYSIS, DIFFERENTIAL EQUATIONS, NUMERICAL METHODS AND PROCEDURES.

Subject Categories : Numerical Mathematics

Distribution Statement : APPROVED FOR PUBLIC RELEASE