On the stability of Scott-Zhang type operators and application to multilevel preconditioning in fractional diffusion
Fuente:
arXiv
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2019
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866917731380494336 |
|---|---|
| author | Faustmann, Markus Melenk, Jens Markus Parvizi, Maryam |
| author_facet | Faustmann, Markus Melenk, Jens Markus Parvizi, Maryam |
| contents | We provide an endpoint stability result for Scott-Zhang type operators in Besov spaces. For globally continuous piecewise polynomials these are bounded from $H^{3/2}$ into $B^{3/2}_{2,\infty}$; for elementwise polynomials these are bounded from $H^{1/2}$ into $B^{1/2}_{2,\infty}$. As an application, we obtain a multilevel decomposition based on Scott-Zhang operators on a hierarchy of meshes generated by newest vertex bisection with equivalent norms up to (but excluding) the endpoint case. A local multilevel diagonal preconditioner for the fractional Laplacian on locally refined meshes with optimal eigenvalue bounds is presented. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1912_09160 |
| institution | arXiv |
| publishDate | 2019 |
| record_format | arxiv |
| spellingShingle | On the stability of Scott-Zhang type operators and application to multilevel preconditioning in fractional diffusion Faustmann, Markus Melenk, Jens Markus Parvizi, Maryam Numerical Analysis We provide an endpoint stability result for Scott-Zhang type operators in Besov spaces. For globally continuous piecewise polynomials these are bounded from $H^{3/2}$ into $B^{3/2}_{2,\infty}$; for elementwise polynomials these are bounded from $H^{1/2}$ into $B^{1/2}_{2,\infty}$. As an application, we obtain a multilevel decomposition based on Scott-Zhang operators on a hierarchy of meshes generated by newest vertex bisection with equivalent norms up to (but excluding) the endpoint case. A local multilevel diagonal preconditioner for the fractional Laplacian on locally refined meshes with optimal eigenvalue bounds is presented. |
| title | On the stability of Scott-Zhang type operators and application to multilevel preconditioning in fractional diffusion |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/1912.09160 |