On error estimator and adaptivity in the meshless Galerkin boundary node method

Authors:
Xiaolin Li
Affiliations:
College of Mathematics Science, Chongqing Normal University, Chongqing, People's Republic of China 400047
Venue:
Computational Mechanics
Year:
2012

Citing 6
Cited 0

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Abstract

In this article, a simple a posteriori error estimator and an effective adaptive refinement process for the meshless Galerkin boundary node method (GBNM) are presented. The error estimator is formulated by the difference between the GBNM solution itself and its L 2-orthogonal projection. With the help of a localization technique, the error is estimated by easily computable local error indicators and hence an adaptive algorithm for h-adaptivity is formulated. The convergence of this adaptive algorithm is verified theoretically in Sobolev spaces. Numerical examples involving potential and elasticity problems are also provided to illustrate the performance and usefulness of this adaptive meshless method.