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

Abstract

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-BabuskaBrezzi 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.

A Stabilized Hybrid Discontinuous Galerkin Method for Nearly Incompressible Linear Elasticity Problem

“…Robustness, local conservation and flexibility for implementing h and padaptivity strategies are well known advantages of DG methods stemming from the use of finite element spaces consisting of discontinuous piecewise polynomials. A natural connection between DG formulations and hybrid methods have been exploited successfully in many problems [11][12][13][14][15] and they are still being developed. These hybrid formulations have improved stability, robustness and flexibility of the DG methods with reduced complexity and computational cost.…”