A dual-mixed finite element method for nonlinear incompressible elasticity with mixed boundary conditions
In this paper we consider the Hu-Washizu principle and propose a new dual-mixed finite element method for nonlinear incompressible plane elasticity with mixed boundary conditions. The approach extends a related previous work on the Dirichlet problem and imposes the Neumann (essential) boundary condi...
| Autor Principal: | Gatica, Gabriel N. |
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| Otros Autores: | Gatica, Luis F., Stephan, Ernst |
| Formato: | Artículo |
| Idioma: | English |
| Publicado: |
A dual-mixed finite element method for nonlinear incompressible elasticity with mixed boundary conditions
2015
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| Materias: | |
| Acceso en línea: |
Computer Methods in Applied Mechanics and Engineering 196 |
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| Sumario: |
In this paper we consider the Hu-Washizu principle and propose a new dual-mixed finite element method for nonlinear incompressible plane elasticity with mixed boundary conditions. The approach extends a related previous work on the Dirichlet problem and imposes the Neumann (essential) boundary condition in a weak sense by means of an additional Lagrange multiplier. The resulting variational formulation becomes a twofold saddle point operator equation which, for convenience of the subsequent analysis, is shown to be equivalent to a nonlinear threefold saddle point problem. In this way, a slight generalization of the classical Babuška–Brezzi theory is applied to show the well-posedness of the continuous and discrete formulations, and to derive the corresponding a priori error estimates. In particular, the classical PEERS space is suitably enriched to define the associated Galerkin scheme. Next, we develop a local problems-based a posteriori error analysis and derive an implicit reliable and quasi-efficient estimate, and a fully explicit reliable one. Finally, several numerical results illustrating the good performance of the explicit a posteriori estimate for the adaptive computation of the discrete solutions are provided. |
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