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\(h\)- and \(p\)-adaptive boundary element methods. (English) Zbl 0770.65076

For 2-D potential and elasticity problems described by an boundary integral equation adaptive boundary element methods are proposed. Based on approximation theory, an a posteriori error estimate for the boundary element solution is developed. Both \(h\)-version and \(p\)-version of the estimate are studied.
Linear elements are used in the \(h\)-version, on the other hand, hierarchical shape functions are employed for the implementation of the \(p\)-version. A number of numerical examples is given, demonstrating the success of the techniques developed in the paper.

MSC:

65N38 Boundary element methods for boundary value problems involving PDEs
65N15 Error bounds for boundary value problems involving PDEs
74B05 Classical linear elasticity
31A30 Biharmonic, polyharmonic functions and equations, Poisson’s equation in two dimensions
35J40 Boundary value problems for higher-order elliptic equations
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