Locking-Free Cg-Type Finite Element Solvers For Linear Elasticity On Simplicial Meshes

This paper presents numerical methods for solving linear elasticity on simplicial meshes based on enrichment of Lagrangian bilinear/trilinear finite elements. This is a renovated use of the classical 1st order Bernardi-Raugel spaces, which were originally designed for Stokes flow. A projection to the elementwise constant space is employed to handle the dilation (divergence of displacement) in the strain-div formulation. Mixed (both Dirichlet and Neumann) boundary conditions are considered for error estimates in the energy-norm and the L-2-norms of displacement and stress. Rigorous analysis and numerical experiments demonstrate that these methods are free of Poisson-locking. Renovation of other Stokes element pairs to linear elasticity is also examined.