Ye, T. Q.; Zhang, Daming; Li, S.; Cheng, J. L. \(h\)- and \(p\)-adaptive boundary element methods. (English) Zbl 0770.65076 Adv. Eng. Softw. 15, No. 3-4, 217-222 (1992). 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. Reviewer: J.Vaníček (Praha) Cited in 1 Document 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 Keywords:potential problem; elasticity problems; boundary integral equation; error estimate; \(h\)-version; \(p\)-version; hierarchical shape functions; numerical examples; adaptive boundary element methods PDFBibTeX XMLCite \textit{T. Q. Ye} et al., Adv. Eng. Softw. 15, No. 3--4, 217--222 (1992; Zbl 0770.65076) Full Text: DOI