We devise variants of classical nonconforming methods for symmetric elliptic problems. These variants differ from the original ones only by transforming discrete test functions into conforming functions before applying the load functional. We derive and discuss conditions on these transformations implying that the ensuing method is quasi-optimal and that its quasi-optimality constant coincides with its stability constant. As applications, we consider the approximation of the Poisson problem with Crouzeix--Raviart elements and higher order counterparts and the approximation of the biharmonic problem with Morley elements. In each case, we construct a computationally feasible transformation and obtain a quasi-optimal method with respect to the piecewise energy norm on a shape regular mesh.
Quasi-optimal nonconforming methods for symmetric elliptic problems. II-Overconsistency and classical nonconforming elements / A. Veeser, P. Zanotti. - In: SIAM JOURNAL ON NUMERICAL ANALYSIS. - ISSN 0036-1429. - 57:1(2019), pp. 266-292.
Quasi-optimal nonconforming methods for symmetric elliptic problems. II-Overconsistency and classical nonconforming elements
A. Veeser;P. Zanotti
2019
Abstract
We devise variants of classical nonconforming methods for symmetric elliptic problems. These variants differ from the original ones only by transforming discrete test functions into conforming functions before applying the load functional. We derive and discuss conditions on these transformations implying that the ensuing method is quasi-optimal and that its quasi-optimality constant coincides with its stability constant. As applications, we consider the approximation of the Poisson problem with Crouzeix--Raviart elements and higher order counterparts and the approximation of the biharmonic problem with Morley elements. In each case, we construct a computationally feasible transformation and obtain a quasi-optimal method with respect to the piecewise energy norm on a shape regular mesh.File | Dimensione | Formato | |
---|---|---|---|
SiamJNumerAnalVol57No1Pp266-292.pdf
accesso riservato
Tipologia:
Publisher's version/PDF
Dimensione
540.18 kB
Formato
Adobe PDF
|
540.18 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.