# Dual mixed finite element method of the elasticity and elastodynamic problems: a priori and a posteriori error analysis.

Abstract : In this work, we study the refinement of grids for the dual mixed finite element method for two types of problems: the first one concerns the linear elasticity problem and the second one the linear elastodynamic problem.

For these two types of problems and in nonregular domains, the mixed finite element methods analyzed until present relate to the primal mixed methods. Here, we analyze the dual mixed formulation for both linear elasticity and linear elastodynamic problems.
For the elasticity problem, we are concerned firstly by an a priori error analysis when using finite element approximation by stabilized $BDM_1$ element.
Then, we make an a posteriori error analysis for the dual mixed finite element method for both a simply and a multiply connected domain. In fact we establish a residue based reliable and eff\mbox{}icient error estimator for the dual mixed finite element method. This estimator is then used in an adaptive algorithm for automatic mesh refinement.
For the elastodynamic problem, we make an a priori error analysis when using the same finite element as for the elasticity problem, using a dual mixed formulation for the discretization in the spatial variables and the explicit or implicit Newmark scheme for the discretization in time. By adequate refinement rules on the regular family of triangulations we derive optimal a priori error estimates for the explicit-in-time and implicit-in-time numerical schemes.
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https://tel.archives-ouvertes.fr/tel-00136422
Contributor : Lahcen Boulaajine <>
Submitted on : Tuesday, March 13, 2007 - 8:19:21 PM
Last modification on : Friday, March 26, 2021 - 1:58:51 PM
Long-term archiving on: : Tuesday, April 6, 2010 - 10:05:16 PM

### Identifiers

• HAL Id : tel-00136422, version 1

### Citation

Lahcen Boulaajine. Dual mixed finite element method of the elasticity and elastodynamic problems: a priori and a posteriori error analysis.. Mathematics [math]. Université de Valenciennes et du Hainaut-Cambresis, 2006. English. ⟨tel-00136422⟩

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