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- W3081884999 abstract "The $L^2$-orthogonal projection $Pi_h:L^2(Omega)rightarrowmathbb{V}_h$ onto a finite element (FE) space $mathbb{V}_h$ is called $H^1$-stable iff $|nablaPi_h u|_{L^2(Omega)}leq C|u|_{H^1(Omega)}$, for any $uin H^1(Omega)$ with a positive constant $Cneq C(h)$ independent of the mesh size $h>0$. In this work, we discuss local criteria for the $H^1$-stability of adaptively refined meshes. We show that adaptive refinement strategies for quadrilateral meshes in 2D (Q-RG and Q-RB), introduced originally in Bank et al. 1982 and Kobbelt 1996, are $H^1$-stable for FE spaces of polynomial degree $p=2,ldots,9$." @default.
- W3081884999 created "2020-09-08" @default.
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- W3081884999 date "2021-06-29" @default.
- W3081884999 modified "2023-10-16" @default.
- W3081884999 title "H 1-stability of the L2-projection onto finite element spaces on adaptively refined quadrilateral meshes" @default.
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- W3081884999 doi "https://doi.org/10.1093/imanum/drab048" @default.
- W3081884999 hasPublicationYear "2021" @default.
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