A simple nonconforming bilinear element for the elasticity problem

• We look at the mixed non-conforming Rannacher-Turek (RT) element from the point of view of discontinuous Galerkin methods. In the case of the elasticity operator, for which the RT element is not stable in that it does not (in general) fulfill a discrete horn's inequality, the discontinuous framework naturally suggests the appearance of (weakly consistent) stabilization terms. We thus obtain a modifed, stable and locking free, version of the RT element for the elasticity problem. We also give some implementation aspects of the element. Numerical results are included.

Nyckelord

nonconforming element

Nitsche's method

discontinuous finite element method

incompressible problems

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