| Autor: |
Horger, T., Melenk, J. M., Wohlmuth, B. |
| Rok vydání: |
2015 |
| Předmět: |
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| Zdroj: |
Computing and Visualization in Science, 16 (2013), pp. 231--246 |
| Druh dokumentu: |
Working Paper |
| DOI: |
10.1007/s00791-015-0237-z |
| Popis: |
We show that optimal $L^2$-convergence in the finite element method on quasi-uniform meshes can be achieved if, for some $s_0 > 1/2$, the boundary value problem has the mapping property $H^{-1+s} \rightarrow H^{1+s}$ for $s \in [0,s_0]$. The lack of full elliptic regularity in the dual problem has to be compensated by additional regularity of the exact solution. Furthermore, we analyze for a Dirichlet problem the approximation of the normal derivative on the boundary without convexity assumption on the domain. We show that (up to logarithmic factors) the optimal rate is obtained. |
| Databáze: |
arXiv |
| Externí odkaz: |
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