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.
Positivity Preserving Gradient Approximation with Linear Finite Elements / A. Veeser. - In: COMPUTATIONAL METHODS IN APPLIED MATHEMATICS. - ISSN 1609-4840. - 19:2(2018), pp. 295-310. [10.1515/cmam-2018-0017]
Positivity Preserving Gradient Approximation with Linear Finite Elements
A. Veeser
2018
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.File | Dimensione | Formato | |
---|---|---|---|
sub1.pdf
accesso aperto
Tipologia:
Pre-print (manoscritto inviato all'editore)
Dimensione
304.99 kB
Formato
Adobe PDF
|
304.99 kB | Adobe PDF | Visualizza/Apri |
[Computational Methods in Applied Mathematics] Positivity Preserving Gradient Approximation with Linear Finite Elements.pdf
accesso riservato
Tipologia:
Publisher's version/PDF
Dimensione
759.69 kB
Formato
Adobe PDF
|
759.69 kB | Adobe PDF | Visualizza/Apri Richiedi una copia |
Pubblicazioni consigliate
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.