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.
@article{702976,
title = {A multi-space error estimation approach for meshfree methods},
booktitle = {Application of Mathematics 2015},
series = {GDML\_Books},
publisher = {Institute of Mathematics CAS},
address = {Prague},
year = {2015},
pages = {194-205},
zbl = {06669930},
url = {http://dml.mathdoc.fr/item/702976}
}
Rüter, Marcus; Chen, Jiun-Shyan. A multi-space error estimation approach for meshfree methods, dans Application of Mathematics 2015, GDML_Books, (2015), pp. 194-205. http://gdmltest.u-ga.fr/item/702976/