Fictitious domain method with boundary value correction using penalty-free Nitsche method
| Autor: | Boiveau, Thomas, Burman, Erik, Claus, Susanne, Larson, Mats G. |
|---|---|
| Rok vydání: | 2016 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | 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 $H^1$-norm and estimates suboptimal by $\mathcal{O}(h^{\frac12})$ in the $L^2$-norm. The suboptimality is due to the lack of adjoint consistency of our formulation. Numerical results are provided to corroborate the theoretical study. Comment: 29 pages, 10 figures |
| Databáze: | arXiv |
| Externí odkaz: |
|