Recent studies on adaptive boundary element methods

Abstract This is a review of the recent studies on adaptive mesh refinement schemes for boundary element methods. We suppose that the adaptive mesh refinement schemes are constructed of error estimation, adaptive tactics and mesh refinement processes. The error estimation process estimates the error of numerical solution. The existing studies on error estimation are classified into residual type, interpolation error type, boundary integral equation error type, and others. The adaptive tactics process selects boundary elements to be refined and the related mesh refinement scheme. The mesh refinement process generates the data of the refined mesh. The existing studies on mesh refinement are classified into h-, p- and r-refinement, and their combination schemes. Various schemes proposed will be discussed from these three points of view.

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