On the Sobolev and $L^p$-Stability of the $L^2$-Projection

Diening L, Storn J, Tscherpel T (2021)
SIAM Journal on Numerical Analysis 59(5): 2571-2607.

Zeitschriftenaufsatz | Veröffentlicht | 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 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.
Stichworte
$L^2$-projection
Erscheinungsjahr
2021
Zeitschriftentitel
SIAM Journal on Numerical Analysis
Band
59
Ausgabe
5
Seite(n)
2571-2607
ISSN
0036-1429
eISSN
1095-7170
Page URI
https://pub.uni-bielefeld.de/record/2957935

Zitieren

Diening L, Storn J, Tscherpel T. On the Sobolev and $L^p$-Stability of the $L^2$-Projection. SIAM Journal on Numerical Analysis. 2021;59(5):2571-2607.
Diening, L., Storn, J., & Tscherpel, T. (2021). On the Sobolev and $L^p$-Stability of the $L^2$-Projection. SIAM Journal on Numerical Analysis, 59(5), 2571-2607. https://doi.org/10.1137/20M1358013
Diening, L., Storn, J., and Tscherpel, T. (2021). On the Sobolev and $L^p$-Stability of the $L^2$-Projection. SIAM Journal on Numerical Analysis 59, 2571-2607.
Diening, L., Storn, J., & Tscherpel, T., 2021. On the Sobolev and $L^p$-Stability of the $L^2$-Projection. SIAM Journal on Numerical Analysis, 59(5), p 2571-2607.
L. Diening, J. Storn, and T. Tscherpel, “On the Sobolev and $L^p$-Stability of the $L^2$-Projection”, SIAM Journal on Numerical Analysis, vol. 59, 2021, pp. 2571-2607.
Diening, L., Storn, J., Tscherpel, T.: On the Sobolev and $L^p$-Stability of the $L^2$-Projection. SIAM Journal on Numerical Analysis. 59, 2571-2607 (2021).
Diening, Lars, Storn, Johannes, and Tscherpel, Tabea. “On the Sobolev and $L^p$-Stability of the $L^2$-Projection”. SIAM Journal on Numerical Analysis 59.5 (2021): 2571-2607.

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