Issue |
ESAIM: M2AN
Volume 40, Number 1, January-February 2006
|
|
---|---|---|
Page(s) | 1 - 28 | |
DOI | https://doi.org/10.1051/m2an:2006003 | |
Published online | 23 February 2006 |
Analysis of a new augmented mixed finite element method
for linear elasticity allowing
-
-
approximations
GI 2MA, Departamento de Ingeniería Matemática,
Universidad de Concepción, Casilla 160-C, Concepción, Chile. ggatica@ing-mat.udec.cl
Received:
4
December
2004
We present a new stabilized mixed finite element method for the linear elasticity problem in . The
approach is based on the introduction of Galerkin least-squares terms arising from the constitutive and
equilibrium equations, and from the relation defining the rotation in terms of the displacement. We show that
the resulting augmented variational formulation and the associated Galerkin scheme are well posed, and that
the 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 lowest
order for the stress tensor, piecewise linear elements for the displacement, and piecewise constants for the
rotation. In the case of mixed boundary conditions, the essential one (Neumann) is imposed weakly, which
yields the introduction of the trace of the displacement as a suitable Lagrange multiplier. This trace is
then approximated by piecewise linear elements on an independent partition of the Neumann boundary whose mesh
size needs to satisfy a compatibility condition with the mesh size associated to the triangulation of the
domain. Several numerical results illustrating the good performance of the augmented mixed finite element
scheme in the case of Dirichlet boundary conditions are also reported.
Mathematics Subject Classification: 65N12 / 65N15 / 65N30 / 74B05
Key words: Mixed-FEM / augmented formulation / linear elasticity / locking-free.
© EDP Sciences, SMAI, 2006
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