Boundary Integral Equations and A Posteriori Error Estimates

Adaptive methods have been rapidly developed and applied in many fields of scientific and engineering computing. Reliable and efficient a posteriori error estimates play key roles for both adaptive finite element and boundary element methods. The aim of this paper is to develop a posteriori error es...

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Bibliographic Details
Published in:Tsinghua science and technology 2005-02, Vol.10 (1), p.35-42
Main Authors: Yu, Dehao, Zhao, Longhua
Format: Article
Language:English
Subjects:
a posteriori error estimate
boundary integral equation
hyper-singular residual
natural boundary reduction
pseudo-differential operator
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Summary:Adaptive methods have been rapidly developed and applied in many fields of scientific and engineering computing. Reliable and efficient a posteriori error estimates play key roles for both adaptive finite element and boundary element methods. The aim of this paper is to develop a posteriori error estimates for boundary element methods. The standard a posteriori error estimates for boundary element methods are obtained from the classical boundary integral equations. This paper presents hyper-singular a posteriori error estimates based on the hyper-singular integral equations. Three kinds of residuals are used as the estimates for boundary element errors. The theoretical analysis and numerical examples show that the hyper-singular residuals are good a posteriori error indicators in many adaptive boundary element computations.
ISSN:1007-0214
1878-7606
1007-0214
DOI:10.1016/S1007-0214(05)70006-7