Error estimation and h adaptive boundary elements

摘要

This paper deals with error estimation of the boundary element method (BEM) and the h adaptive boundary elements. The various error sources in the BEM are discussed, and the upper bound of the BEM solution error is derived by means of the interpolation error of the BE solution. A new error estimator is presented in the paper by using post-processing data from the standard BEM solutions. Two adaptive algorithms, the standard h adaptive and the h-hierarchical adaptive, are implemented based on direct boundary element method for two-dimensional elasticity problems. A few numerical examples are used to compare the accuracy of the proposed adaptive algorithm, as well as the error estimator. The stability of the BEM system matrix, which may deteriorate due to the introduction of h-hierarchical interpolation functions, has also been studied.