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On adaptive finite element methods for Fredholm integral equations of the second kind

Journal article
Authors Mohammad Asadzadeh
Kenneth Eriksson
Published in SIAM Journal on Numerical Analysis
Volume 31
Issue 3
Pages 831-855
Publication year 1994
Published at Department of Mathematics
Pages 831-855
Language en
Keywords Fredholm integral equation, potential problems, adaptive finite element method, a posteriors and a priori error estimates
Subject categories Applied mathematics

Abstract

A posteriors and a priori error estimates are derived for a finite element discretization of a Fredholm integral equation of the second kind. A reliable and efficient adaptive algorithm is then designed for a specific computational goal with applications to potential problems. The reliability of the algorithm is guaranteed by the a posteriors error estimate and the efficiency follows from the a priori error estimate, which shows that the a posteriors error bound is sharp

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