| 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 |
| Year:
|
|
| 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 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/702976 |
| . |
