Error estimation and adaptive procedures based on superconvergent patch recovery (SPR) techniques |
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Authors: | N E Wiberg F Abdulwahab X D Li |
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Affiliation: | (1) Department of Structural Mechanics, Chalmers University of Technology, 412 96 Goteborg, Sweden |
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Abstract: | Summary The paper discusses error estimation and adaptive finite element procedures for elasto-static and dynamic problems based on
superconvergent patch recovery (SPR) techniques. The SPR is a postprocessing procedure to obtain improved finite element solutions
by the least squares fitting of superconvergent stresses at certain sampling points in local patches. An enhancement of the
original SPR by accounting for the equilibirum equations and boundary conditions is proposed. This enhancement improves the
quality of postprocessed solutions considerably and thus provides an even more effective error estimate. The patch configuration
of SPR can be either the union of elements surrounding a vertex node, thenode patch, or, the union of elements surrounding an element, theelement patch. It is shown that these two choices give normally comparable quality of postprocessed solutions. The paper is also concerned
with the application of SPR techniques to a wide range of problems. The plate bending problem posted in mixed form where force
and displacement variables are simultaneously used as unknowns is considered. For eigenvalue problems, a procedure of improving
eigenpairs and error estimation of the eigenfrequency is presented. A postprocessed type of error estimate and an adaptive
procedure for the semidiscrete finite element method are discussed. It is shown that the procedure is able to update the spatial
mesh and the time step size so that both spatial and time discretization errors are controlled within specified tolerances.
A discontinuous Galerkin method for solving structural dynamics is also presented. |
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