A Stabilized Hybrid-Mixed Finite Element Formulation for the Elasticity Problems

Abstract

A stabilized hybrid dual-mixed finite element formulation is proposed to the elasticity problem in displacement and stress fields and a Lagrange multiplier identified a priori as the trace of the displacement field on the edges of the elements. The stabilization mechanisms, used to overcome the local compatibility condition (Ladyzhenskaya-Babuska-Brezzi condition), are activated by adding least squares residual forms of the governing equations in domain and on element boundary. Features of the formulation such as consistency, stability and local conservation are discussed. Numerical results for problems with smooth solution confirming optimal rates of convergence are presented.