Quasi-optimal nonconforming methods for symmetric elliptic problems. II-Overconsistency and classical nonconforming elements
Articolo
Data di Pubblicazione:
2019
Citazione:
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.
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.
Tipologia IRIS:
01 - Articolo su periodico
Keywords:
quasi-optimality; nonconforming elements; Crouzeix--Raviart elements; Morley element
Elenco autori:
A. Veeser, P. Zanotti
Link alla scheda completa: