Exponential meshes and $\mathcal{H}$-matrices
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2022
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| _version_ | 1866913442967846912 |
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| author | Angleitner, Niklas Faustmann, Markus Melenk, Jens Markus |
| author_facet | Angleitner, Niklas Faustmann, Markus Melenk, Jens Markus |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2203_09925 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Exponential meshes and $\mathcal{H}$-matrices Angleitner, Niklas Faustmann, Markus Melenk, Jens Markus Numerical Analysis 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. |
| title | Exponential meshes and $\mathcal{H}$-matrices |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2203.09925 |