Computational competition of symmetric mixed FEM in linear elasticity

The Navier–Lamé equation for linear elasticity has evoked the design of various non-standard finite element methods (FEM) in order to overcome the locking phenomenon. Recent developments of Arnold and Winther in 2002 involve a stable mixed method which strongly fulfils the symmetry constraint. Subsequently, two H(div) non-conforming symmetric mixed methods arose. This paper comments on the implementation of all those mixed FEM and provides a numerical comparison of the different symmetric mixed schemes for linear elasticity. The computational survey also includes the low-order elements of weak symmetry (PEERS), the non-conforming Kouhia and Stenberg (KS) elements plus the conforming displacement Pk-FEM for k = 1, 2, 3, 4. Numerical experiments confirm the theoretical convergence rates for sufficiently smooth solutions and illustrate the superiority of the symmetric MFEM amongst the methods of second or third order.