Error estimation and adaptive mesh refinement in boundary element method, an overview

摘要

Further to the previous review article (Adv Engng Software 19(1 ) (1994) 21 --32), this paper reviews more recent studies on the same subject by citing more than one hundred papers. The adaptive mesh refinement process is composed of three processes; the error estimation, the adaptive tactics and the mesh refinement processes. Therefore, in this paper, the existing studies are classified and discussed according to the processes. The error estimation schemes are classified into the residual-type, the interpolation-type, the integral equation-type, the node sensitivity- type and the solution difference type. The mesh refinement schemes are classified into h-, p-, r-schemes and the others. The adaptive tactics are closely related to the mesh refinement schemes. Therefore, they are discussed individually. The discussion presented herein is an extension of the previous article and focuses our principal attention on the following points. Some interesting studies for the error estimation scheme are added; e.g. new schemes named as ‘nodal design sensitivity', ‘hyper-singular residual type' and ‘solution difference type'. Some studies for the adaptive tactics are added; e.g. the tactics based on the convergence property of the error, the extension of the extended error indicator to r- and hr-adaptive schemes and so on.