An augmented mixed finite element method for 3D linear elasticity problems

Gatica, GN; Marquez, A; Meddahi S.

Abstract

In this paper we introduce and analyze a new augmented mixed finite element method for linear elasticity problems in 3D. Our approach is an extension of a technique developed recently for plane elasticity, which is based on the introduction of consistent terms of Galerkin least-squares type. We consider non-homogeneous and homogeneous Dirichlet boundary conditions and prove that the resulting augmented variational formulations lead to strongly coercive bilinear forms. In this way, the associated Galerkin schemes become well posed for arbitrary choices of the corresponding finite element subspaces. In particular, Raviart-Thomas spaces of order 0 for the stress tensor, continuous piecewise linear elements for the displacement, and piecewise constants for the rotation can be utilized. Moreover, we show that in this case the number of unknowns behaves approximately as 9.5 times the number of elements (tetrahedrons) of the triangulation, which is cheaper, by a factor of 3, than the classical P E E R S in 3D. Several numerical results illustrating the good performance of the augmented schemes are provided. © 2009 Elsevier B.V. All rights reserved.

Más información

Título según WOS: An augmented mixed finite element method for 3D linear elasticity problems
Título según SCOPUS: An augmented mixed finite element method for 3D linear elasticity problems
Título de la Revista: JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
Volumen: 231
Número: 2
Editorial: ELSEVIER SCIENCE BV
Fecha de publicación: 2009
Página de inicio: 526
Página final: 540
Idioma: English
URL: http://linkinghub.elsevier.com/retrieve/pii/S0377042709002349
DOI:

10.1016/j.cam.2009.03.018

Notas: ISI, SCOPUS