Positivity Preserving Gradient Approximation with Linear Finite Elements
Abstract: 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.
- Location
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Deutsche Nationalbibliothek Frankfurt am Main
- Extent
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Online-Ressource
- Language
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Englisch
- Bibliographic citation
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Positivity Preserving Gradient Approximation with Linear Finite Elements ; volume:19 ; number:2 ; year:2019 ; pages:295-310 ; extent:16
Computational methods in applied mathematics ; 19, Heft 2 (2019), 295-310 (gesamt 16)
- Creator
- DOI
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10.1515/cmam-2018-0017
- URN
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urn:nbn:de:101:1-2410251708000.412208886317
- Rights
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Open Access; Der Zugriff auf das Objekt ist unbeschränkt möglich.
- Last update
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15.08.2025, 7:23 AM CEST
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