Boiveau, T;
Burman, E;
Claus, S;
Larson, MG;
(2017)
Fictitious domain method with boundary value correction using penalty-free Nitsche method.
Journal of Numerical Mathematics
10.1515/jnma-2016-1103.
(In press).
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Abstract
In this paper, we consider a fictitious domain approach based on a Nitsche type method without penalty. To allow for high order approximation using piecewise affine approximation of the geometry we use a boundary value correction technique based on Taylor expansion from the approximate to the physical boundary. To ensure stability of the method a ghost penalty stabilization is considered in the boundary zone. We prove optimal error estimates in the H1-norm and estimates suboptimal by O(h12) q in the L2-norm. The suboptimality is due to the lack of adjoint consistency of our formulation. Numerical results are provided to corroborate the theoretical study.
| Type: | Article |
|---|---|
| Title: | Fictitious domain method with boundary value correction using penalty-free Nitsche method |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1515/jnma-2016-1103 |
| Publisher version: | https://doi.org/10.1515/jnma-2016-1103 |
| Language: | English |
| Additional information: | © 2017 by Walter de Gruyter Berlin/Boston. This version is the version of record. For information on re-use, please refer to the publisher’s terms and conditions. |
| Keywords: | Nitsche’s method, fictitious domain method, boundary value correction, 65N12, 65N30, 65N85 |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Mathematics |
| URI: | https://discovery.ucl.ac.uk/id/eprint/1523448 |
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