Nonconforming finite element methods without numerical locking
Many authors have studied different methods to cure numerical locking which can occur in the approximation of elliptic problems which depend on a small parameter \(\varepsilon\) (very thin plates or shells, nearly incompressible elasticity, heat transfer problems with very small ratio of conductivies,\(\dots\)). By using compactness properties proved by \textit{F. Stummel} for nonconforming spaces [RAIRO, Anal. Numer. 14, 81-115 (1980; Zbl 0456.65061)] the authors extend to the nonconforming case some results obtained by \textit{D. Chenais} and \textit{J.-C. Paumier} [Numer. Math. 67, No. 4, 427-440 (1994; Zbl 0798.73054) in the prevention of numerical locking for the conforming finite element method. Results are valid whether numerical integration is used or not. This is a very nice theoretical study including detailed proofs.
scientific article; zbMATH DE number 1247601