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Title: A multi-space error estimation approach for meshfree methods (English)
Author: Rüter, Marcus
Author: Chen, Jiun-Shyan
Language: English
Journal: Application of Mathematics 2015
Volume: Proceedings. Prague, November 18-21, 2015
Issue: 2015
Pages: 194-205
Category: math
Summary: Error-controlled adaptive meshfree methods are presented for both global error measures, such as the energy norm, and goal-oriented error measures in terms of quantities of interest. The meshfree method chosen in this paper is the reproducing kernel particle method (RKPM), since it is based on a Galerkin scheme and therefore allows extensions of quality control approaches as already developed for the finite element method. Our approach of goal-oriented error estimation is based on the well-established technique using an auxiliary dual problem. To keep the formulation general and to add versatility, a multi-space approach is used, where the dual problem is solved numerically using a different approximation space than the one employed in the associated primal problem. This can be realized with meshfree methods at no additional cost. Possible merits of this multi-space approach are discussed and an illustrative numerical example is presented. (English)
Keyword: reproducing kernel particle method (RKPM)
Keyword: meshfree methods
Keyword: goal-oriented error estimation
Keyword: dual problem
MSC: 65N15
MSC: 65N50
MSC: 74B05
MSC: 74R10
idZBL: Zbl 06669930
Date available: 2017-02-14T10:25:52Z
Last updated: 2017-03-20
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