RAFILIPOJAONA

We study a dual mixed formulation of the elasticity system in a polygonal domain of the plane with mixed boundary conditions and its numerical approximation. The (essential) Neumann boundary conditions (or traction boundary condition) are imposed using a discontinuous Lagrange multiplier corresponding to the trace of the displacement field. Moreover, a strain tensor is introduced as a new unknown and its symmetry is relaxed, also by the use of a Lagrange multiplier (the rotation). The singular behaviour of the solution requires us to use refined meshes to restore optimal rates of convergence. Uniform error estimates in the Lamé coefficient λ are obtained for large λ. The hybridization of the problem is performed and numerical tests are presented confirming our theoretical results.

Abstract This paper is concerned with a dual mixed formulation of the Navier — Stokes system in a polygonal domain of the plane with mixed boundary conditions and its numerical approximation. The Neumann boundary condition is imposed using a Lagrange multiplier corresponding to the velocity field. Moreover, the strain tensor and the antisymmetric gradient tensor (vorticity), quantities of practical interest, are introduced as new unknowns. The problem is then approximated by a mixed finite element method. Quasi-optimal error estimates are finally obtained using refined meshes near singular corners.