Incompatible Bubbles: A non-conforming finite element formulation for linear elasticity

A non-conforming finite element formulation, the Incompatible Bubbles method, is proposed for the problem of linear elasticity. As the classical Incompatible Modes method, the proposed formulation is based on an enrichment of the Galerkin solution space with non-conforming functions, the incompatible bubbles. In fact, the two formulations coincide in the particular case of non-distorted meshes. The advantage of the new formulation is that by a careful choice of the bubbles some of the “variational crimes” of the classical method become unnecessary for convergence, as the analysis reveals. Also, the relationship of the proposed method with more recent subgrid scale finite element formulations is investigated. Numerical examples illustrating the performance of the method are provided.