Interpolation operator on negative Sobolev spaces

Autor:	Diening, Lars, Storn, Johannes, Tscherpel, Tabea
Rok vydání:	2023
Předmět:	Computational Mathematics Algebra and Number Theory 65D05 65M15 65N15 65N30 Applied Mathematics FOS: Mathematics Mathematics - Numerical Analysis Numerical Analysis (math.NA)
Zdroj:	PUB-Publications at Bielefeld University
ISSN:	1088-6842 0025-5718
Popis:	We introduce a Scott–Zhang type projection operator mapping to Lagrange elements for arbitrary polynomial order. In addition to the usual properties, this operator is compatible with duals of first order Sobolev spaces. More specifically, it is stable in the corresponding negative norms and allows for optimal rates of convergence. We discuss alternative operators with similar properties. As applications of the operator we prove interpolation error estimates for parabolic problems and smoothen rough right-hand sides in a least squares finite element method.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_dedup___::3d53eac942fbdd4add2d0d0d6bac4f6d https://doi.org/10.1090/mcom/3824 Zobrazit plný text záznamu