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Summary: A POSTERIORI ERROR ESTIMATES FOR
FOURTH-ORDER ELLIPTIC PROBLEMS
Slimane Adjerid
Department of Mathematics
and
Interdisciplinary Center for Applied Mathematics
Virginia Polytechnic Institute and State University
Blacksburg, VA 24061
Abstract
We extend the dichotomy principle of Babuska and Yu [26, 27] and Adjerid et
al. [3, 4] for estimating the finite element discretization error to fourth-order elliptic
problems. We show how to construct a posteriori error estimates from jumps of the
third partial derivatives of the finite element solution when the finite element space
consists of piecewise polynomials of odd degree and from the interior residuals for
even degree approximations on meshes of square elements. These estimates are
shown to converge to the true error under mesh refinement. We also show that
these a posteriori error estimates are asymptotically correct for more general finite
element spaces. Computational results from several examples show that the error
estimates are accurate and efficient on rectangular meshes.
1 Introduction
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