Positivity Preserving Gradient Approximation with Linear Finite Elements

Autor:	Andreas Veeser
Rok vydání:	2018
Předmět:	010101 applied mathematics Computational Mathematics Numerical Analysis Applied Mathematics Mathematical analysis 010103 numerical & computational mathematics 0101 mathematics 01 natural sciences Finite element method Mathematics
Zdroj:	Computational Methods in Applied Mathematics. 19:295-310
ISSN:	1609-9389 1609-4840
DOI:	10.1515/cmam-2018-0017
Popis:	Preserving positivity precludes that linear operators onto continuous piecewise affine functions provide near best approximations of gradients. Linear interpolation thus does not capture the approximation properties of positive continuous piecewise affine functions. To remedy, we assign nodal values in a nonlinear fashion such that their global best error is equivalent to a suitable sum of local best errors with positive affine functions. As one of the applications of this equivalence, we consider the linear finite element solution to the elliptic obstacle problem and derive that its error is bounded in terms of these local best errors.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::f7c3984fdae04580bb0ad2ed497a8437 https://doi.org/10.1515/cmam-2018-0017 Zobrazit plný text záznamu