ARTk−Pkapproximation for linear elasticity yielding a brokenH(div)convergent postprocessed stress

Abstract

We present a non-standard mixed finite element method for the linear elasticity problem in R n with non-homogeneous Dirichlet boundary conditions. More precisely, our approach is based on a simplified interpretation of the pseudostress–displacement formulation originally proposed in Arnold and Falk (1988), which does not require symmetric tensor spaces in the finite element discretization. We apply the classical Babuška–Brezzi theory to prove that the corresponding continuous and discrete schemes are well-posed. In particular, Raviart–Thomas spaces of order k ≥ 0 for the pseudostress and piecewise polynomials of degree ≤ k for the displacement can be utilized. In addition, complementing the results in the aforementioned reference, we introduce a new postprocessing formula for the stress recovering the optimally convergent approximation of the broken H ( div ) -norm. Numerical results confirm our theoretical findings.