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Mathematics of Computation

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On a dimensional reduction method. III. A posteriori error estimation and an adaptive approach

Authors: M. Vogelius and I. Babuška
Journal: Math. Comp. 37 (1981), 361-384
MSC: Primary 65N99; Secondary 65J10
MathSciNet review: 628701
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Abstract: This paper is the last in a series of three which analyze an adaptive approximate approach for solving $(n + 1)$-dimensional boundary value problems by replacing them with systems of equations in n-dimensional space. In this paper we show how to find reliable a posteriori estimates for the error and how these can also be used in the design of an adaptive strategy. Various numerical examples are contained in the paper.

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Article copyright: © Copyright 1981 American Mathematical Society