Accession Number : ADA190296

Title :   A Posteriori Error Estimation in a Finite Element Method for Parabolic Partial Differential Equations.

Descriptive Note : Final rept.,

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

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

PDF Url : ADA190296

Report Date : Dec 1987

Pagination or Media Count : 29

Abstract : Superconvergence properties and quadratic polynomials are used to derive a computationally inexpensive approximation to the spatial component of the error in a piecewise linear finite element method for one-dimensional parabolic partial differential equations. This technique is coupled with time integration schemes of successively higher orders to obtain an approximation of the temporal and total discretization errors. Computational results indicate that these approximations converge to the exact discretization errors as the mesh is refined. The approximate errors are used to control an adaptive mesh refinement strategy. Keywords: Trapezoidal rule; Galerkins method.

Descriptors :   *FINITE ELEMENT ANALYSIS, *PARTIAL DIFFERENTIAL EQUATIONS, *ERROR ANALYSIS, ADAPTIVE SYSTEMS, COMPUTATIONS, ERRORS, ESTIMATES, INTEGRATION, MESH, PARABOLAS, POLYNOMIALS, QUADRATIC EQUATIONS, TIME, ONE DIMENSIONAL, APPROXIMATION(MATHEMATICS), LINEARITY

Subject Categories : Numerical Mathematics

Distribution Statement : APPROVED FOR PUBLIC RELEASE