A STABILIZED HYBRID FINITE ELEMENT METHOD FOR THE LINEAR ELASTICITY PROBLEMS

Abstract

Hybrid formulations have been widely used in computational mechanics associated with primal or mixed finite element methods. Recently, hybrid formulations have been developed associated with Discontinuous Galerkin methods. In this work we propose a new primal hybrid finite element method for linear elasticity. Using a stabilization strategy typical of Discontinuous Galerkin methods, we choose as multiplier the displacement field itself and add stabilization and symmetrization terms to generate a stable and adjoint consistent formulation allowing greater flexibility in the choice of basis functions of approximation spaces for the displacement field and the Lagrange multiplier. The local problems, in the displacement field, can always be solved at the element in favor of the Lagrange multiplier defined on each edge of the elements. The global system is assembled involving only the degrees of freedom associated with the Lagrange multipliers, as usual in a hybrid method, where the continuity on the element edges is imposed weakly. Polynomial bases are adopted to approximate both the displacement field and the Lagrange multipliers considering Lagrangian polynomial base. Result of some numerical experiments are presented to illustrate the potential of the proposed formulation.