We devise new variants of the following nonconforming finite element methods: discontinuous Galerkin methods of fixed arbitrary order for the Poisson problem, the Crouzeix-Raviart interior penalty method for linear elasticity, and the quadratic C0 interior penalty method for the biharmonic problem. Each variant differs from the original method only in the discretization of the right-hand side. Before applying the load functional, a linear operator transforms nonconforming discrete test functions into conforming functions such that stability and consistency are improved. The new variants are thus quasi-optimal with respect to an extension of the energy norm. Furthermore, their quasi-optimality constants are uniformly bounded for shape regular meshes and tend to 1 as the penalty parameter increases.
|Titolo:||Quasi-optimal nonconforming methods for symmetric elliptic problems. III-discontinuous Galerkin and other interior penalty methods|
ZANOTTI, PIETRO (Corresponding)
|Parole Chiave:||C0 interior penalty methods; Crouzeix-Raviart element; Discontinuous elements; Linear elasticity; Quasi-optimality; Numerical Analysis; Computational Mathematics; Applied Mathematics|
|Settore Scientifico Disciplinare:||Settore MAT/05 - Analisi Matematica|
|Data di pubblicazione:||2018|
|Digital Object Identifier (DOI):||10.1137/17M1151675|
|Appare nelle tipologie:||01 - Articolo su periodico|