Title: A feedback finite element method with a posteriori error estimation: Part I. The finite element method and some basic properties of the a posteriori error estimator
Abstract: This paper is the first in a series of two in which we discuss some theoretical and practical aspects of a feedback finite element method for solving systems of linear second-order elliptic partial differential equations (with particular interest in classical linear elasticity). In this first part we introduce some nonstandard finite element spaces, which, though based on the usual square bilinear elements, permit local mesh refinement. The algebraic structure of these spaces and their approximation properties are analyzed. An "equivalent estimator" for the H1 finite element error is developed. In the second paper we shall discuss the asymptotic properties of the estimator and computational experience.
Publication Year: 1987
Publication Date: 1987-03-01
Language: en
Type: article
Indexed In: ['crossref']
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Cited By Count: 281
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