A Stabilized Hybrid Discontinuous Galerkin Method for Nearly Incompressible Linear Elasticity Problem
DOI:
https://doi.org/10.5540/tema.2017.018.03.467Keywords:
Linear elasticity, Discontinuous Galerkin method, Stabilization Hybrid method, Locking freeAbstract
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.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.
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