Hostname: page-component-74656f9884-j7cmm Total loading time: 0 Render date: 2026-11-10T21:05:03.007Z Has data issue: false hasContentIssue false

Analysis of a new augmented mixed finite element methodfor linear elasticity allowing $\mathbb{RT}_0$ - $\mathbb{P}_1$ - $\mathbb{P}_0$ approximations

Published online by Cambridge University Press:  23 February 2006

Gabriel N. Gatica*
Affiliation:
GI2MA, Departamento de Ingeniería Matemática, Universidad de Concepción, Casilla 160-C, Concepción, Chile. ggatica@ing-mat.udec.cl
Get access

Abstract

We present a new stabilized mixed finite element method for the linear elasticity problem in $\mathbb{R}^2$ . Theapproach is based on the introduction of Galerkin least-squares terms arising from the constitutive andequilibrium equations, and from the relation defining the rotation in terms of the displacement. We show thatthe resulting augmented variational formulation and the associated Galerkin scheme are well posed, and thatthe latter becomes locking-free and asymptotically locking-free for Dirichlet and mixed boundary conditions,respectively. In particular, the discrete scheme allows the utilization of Raviart–Thomas spaces of lowestorder for the stress tensor, piecewise linear elements for the displacement, and piecewise constants for therotation. In the case of mixed boundary conditions, the essential one (Neumann) is imposed weakly, whichyields the introduction of the trace of the displacement as a suitable Lagrange multiplier. This trace isthen approximated by piecewise linear elements on an independent partition of the Neumann boundary whose meshsize needs to satisfy a compatibility condition with the mesh size associated to the triangulation of thedomain. Several numerical results illustrating the good performance of the augmented mixed finite elementscheme in the case of Dirichlet boundary conditions are also reported.

Information

Type
Research Article
Copyright
© EDP Sciences, SMAI, 2006

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable