| Autor: |
Angleitner, Niklas, Faustmann, Markus, Melenk, Jens Markus |
| Rok vydání: |
2022 |
| Předmět: |
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| Zdroj: |
Comput. Math. Appl. 130 (2023) pp. 21--40 |
| Druh dokumentu: |
Working Paper |
| DOI: |
10.1016/j.camwa.2022.11.011 |
| Popis: |
In our previous works, we proved that the inverse of the stiffness matrix of an $h$-version finite element method (FEM) applied to scalar second order elliptic boundary value problems can be approximated at an exponential rate in the block rank by $\mathcal{H}$-matrices. Here, we improve on this result in multiple ways: (1) The class of meshes is significantly enlarged and includes certain exponentially graded meshes. (2) The dependence on the polynomial degree $p$ of the discrete ansatz space is made explicit in our analysis. (3) The bound for the approximation error is sharpened, and (4) the proof is simplified. |
| Databáze: |
arXiv |
| Externí odkaz: |
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