@article{YU2005, 
author = {Dehao YU and Longhua ZHAO},
title = {Boundary Integral Equations and A Posteriori Error Estimates},
year = {2005},
journal = {Tsinghua Science and Technology},
volume = {10},
number = {1},
pages = {35-42},
keywords = {boundary integral equation, natural boundary reduction, a posteriori error estimate, hyper-singular residual, pseudo-differential operator},
url = {https://www.sciopen.com/article/10.1016/S1007-0214(05)70006-7},
doi = {10.1016/S1007-0214(05)70006-7},
abstract = {Adaptive methods have been rapidly developed and applied in many fields of scientific and engineering computing. Reliable and efficient a posteriori error estimates play key roles for both adaptive finite element and boundary element methods. The aim of this paper is to develop a posteriori error estimates for boundary element methods. The standard a posteriori error estimates for boundary element methods are obtained from the classical boundary integral equations. This paper presents hyper-singular a posteriori error estimates based on the hyper-singular integral equations. Three kinds of residuals are used as the estimates for boundary element errors. The theoretical analysis and numerical examples show that the hyper-singular residuals are good a posteriori error indicators in many adaptive boundary element computations.}
}