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Host: Mathematical Sciences Research Institute
Organizers: I. Babuska, R. Lazarov, L. Wahlbin
Description:
Superconvergent points are special points at which we can guarantee that the error is of higher order, r+p for some positive p (often, p=1). In principle, one could talk about superconvergence in a particular problem, but most work is aimed at broad classes of problems. Typically one looks for conditions on the finite element mesh that will, together with smoothness assumptions on the partial differential equation, guarantee the existence of superconvergent points. If one knows enough such points one may use them to construct, in a local fashion, an approximation which is better everywhere, a so called patch recovery. This better approximation may then play the role of the "exact" solution and comparing it with the original approximation then furnishes an a posteriori estimate of the error in the original approximation. The problem of a priori identifying superconvergent points is part of the broader problem area of higher order recovery techniques (or postprocessing), and also of the area of a posteriori error estimation. As is common in applied mathematics, the theories cover only a portion of problems and methods of use and interest. E.g., little is known about superconvergence in mixed finite element methods, and some of the general theories do not apply at the boundary of the underlying domain; this is unfortunate since, in many calculations, quantities on the boundary are of main interest. At the workshop, there will be a mix of senior and junior researchers interested in the theoretical and practical aspects of superconvergence and related fields. It is hoped that fundamental practical and theoretical problems can be identified and stock taken of appropriate tools for attacking them.
Date received: October 13, 1998
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