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

Antônio José Boness Santos, C O Faria, Abimael F D Loula

Abstract


In this work, a primal hybrid finite element method for nearly incom pressible linear elasticity problem on triangular meshes is shown. This method consists of coupling local discontinuous Galerkin problems to the primal variable with a global problem for the Lagrange multiplier, which is identified as the trace of the displacement field. Also, a local post-processing technique is used to recover stress approximations with improved rates of convergence in H(div) norm. Numerical studies show that the method is locking free even using equal or different orders for displacement and stress fields and optimal convergence rates are obtained.

Keywords


Linear elasticity, Discontinuous Galerkin method, Stabilization Hybrid method, Locking free

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References


C.O. Faria, A.F.D. Loula, A.J.B. Santos, Primal stabilized hybrid and DG finite

element methods for the linear elasticity problem, Computers & Mathematics with Applications, 68, No. 4 (2014), 486507.

C.O. Faria, A.F.D. Loula, A.J.B. Santos, Stabilized hybridized finite element

method for incompressible and nearly incompressible elasticity, in Proceedings of the XXXIV Iberian Latin American Congress on Computational Methods in Engineering (CILAMCE), Pirenópolis, Goiás, Brasil, 2013.

C.O. Faria, A.J.B. Santos, A.F.D. Loula, Locking-free hybridized fem for incompressible linear elasticity problem, in Proceedings of the XXXVI Iberian Latin American Congress on Computational Methods in Engineering (CILAMCE), Rio de Janeiro, RJ, Brasil, 2015.




DOI: https://doi.org/10.5540/tema.2017.018.03.467

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TEMA - Trends in Applied and Computational Mathematics

A publication of the Brazilian Society of Applied and Computational Mathematics (SBMAC)
ISSN: 1677-1966  (print version),  2179-8451  (online version)

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