On the Sobolev and L^p-Stability of the L^2-projection

Diening L, Storn J, Tscherpel T (2020)
arXiv:2008.01801.

Preprint | Englisch
 
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Abstract / Bemerkung
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 assumptions on the mesh grading in three dimensions we show $W^{1,2}$-stability for all polynomial degrees greater than one. 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.
Erscheinungsjahr
2020
Zeitschriftentitel
arXiv:2008.01801
Page URI
https://pub.uni-bielefeld.de/record/2945927

Zitieren

Diening L, Storn J, Tscherpel T. On the Sobolev and L^p-Stability of the L^2-projection. arXiv:2008.01801. 2020.
Diening, L., Storn, J., & Tscherpel, T. (2020). On the Sobolev and L^p-Stability of the L^2-projection. arXiv:2008.01801
Diening, L., Storn, J., and Tscherpel, T. (2020). On the Sobolev and L^p-Stability of the L^2-projection. arXiv:2008.01801.
Diening, L., Storn, J., & Tscherpel, T., 2020. On the Sobolev and L^p-Stability of the L^2-projection. arXiv:2008.01801.
L. Diening, J. Storn, and T. Tscherpel, “On the Sobolev and L^p-Stability of the L^2-projection”, arXiv:2008.01801, 2020.
Diening, L., Storn, J., Tscherpel, T.: On the Sobolev and L^p-Stability of the L^2-projection. arXiv:2008.01801. (2020).
Diening, Lars, Storn, Johannes, and Tscherpel, Tabea. “On the Sobolev and L^p-Stability of the L^2-projection”. arXiv:2008.01801 (2020).

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