A multi-space error estimation approach for meshfree methods

Rüter, Marcus, and Chen, Jiun-Shyan. "A multi-space error estimation approach for meshfree methods." Application of Mathematics 2015. Prague: Institute of Mathematics CAS, 2015. 194-205. <http://eudml.org/doc/287793>.

@inProceedings{Rüter2015,
abstract = {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.},
author = {Rüter, Marcus, Chen, Jiun-Shyan},
booktitle = {Application of Mathematics 2015},
keywords = {reproducing kernel particle method (RKPM); meshfree methods; goal-oriented error estimation; dual problem},
location = {Prague},
pages = {194-205},
publisher = {Institute of Mathematics CAS},
title = {A multi-space error estimation approach for meshfree methods},
url = {http://eudml.org/doc/287793},
year = {2015},
}

TY - CLSWK
AU - Rüter, Marcus
AU - Chen, Jiun-Shyan
TI - A multi-space error estimation approach for meshfree methods
T2 - Application of Mathematics 2015
PY - 2015
CY - Prague
PB - Institute of Mathematics CAS
SP - 194
EP - 205
AB - 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.
KW - reproducing kernel particle method (RKPM); meshfree methods; goal-oriented error estimation; dual problem
UR - http://eudml.org/doc/287793
ER -