Nonconforming finite element methods without numerical locking

Abstract.

We analyze the numerical approximation of a class of elliptic problems which depend on a small parameter $\varepsilon$. We give a generalization to the nonconforming case of a recent result established by Chenais and Paumier for a conforming discretization. For both the situations where numerical integration is used or not, a uniform convergence in $\varepsilon$ and h is proved, numerical locking being thus avoided. Important tools in the proof of such a result are compactness properties for nonconforming spaces as well as the passage to the limit problem.