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

• Published in: Engineering analysis with boundary elements Vol. 25; no. 7; pp. 479 - 495
• Main Authors: Kita, E., Kamiya, N.
• Format: Journal Article
• Language: English
• Published: Oxford Elsevier Ltd 01.07.2001; Elsevier
• Subjects: Adaptive mesh refinement; Adaptive tactics; Boundary element method; Boundary-integral methods; Computational techniques; Error estimation; Exact sciences and technology; Mathematical methods in physics; Physics; Adaptive tactics; Adaptive mesh refinement; Error estimation; Boundary element method; Estimation error; Singularity; Sensitivity analysis; Refinement method; Numerical method; Adaptive estimation; Automatic mesh generation; Adaptive method; Reviews; Integral equations; Mesh method; Software tools
• ISSN: 0955-7997; 1873-197X
• DOI: 10.1016/S0955-7997(01)00018-2

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.