| Autor: |
Diening, Lars, Storn, Johannes, Tscherpel, Tabea |
| Rok vydání: |
2020 |
| Předmět: |
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| Zdroj: |
SIAM J. Numer. Anal., 59(5), 2021 |
| Druh dokumentu: |
Working Paper |
| DOI: |
10.1137/20M1358013 |
| Popis: |
We show stability of the $L^2$-projection onto Lagrange finite element spaces with respect to (weighted) $L^p$ and $W^{1,p}$-norms for any polynomial degree and for any space dimension under suitable conditions on the mesh grading. This includes $W^{1,2}$-stability in two space dimensions for any polynomial degree and meshes generated by newest vertex bisection. Under realistic but conjectured assumptions on the mesh grading in three dimensions we show $W^{1,2}$-stability for all polynomial degrees. We also propose a modified bisection strategy that leads to better $W^{1,p}$-stability. Moreover, we investigate the stability of the $L^2$-projection onto Crouzeix-Raviart elements. |
| Databáze: |
arXiv |
| Externí odkaz: |
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