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Una nueva formulacion mixta-primal para el problema de la elasticidad lineal en el plano
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A class of new mixed formulations for elasticity is developed and analysed. The formulations are based on the discrete evss method, introduced in the context of incompressible viscoelastic flows by A. Fortin, M. Fortin and co-workers. A key feature is a stabilization term that renders coercive a problem that might not otherwise be so. The focus in this work is on behaviour in the incompressible limit and the goal is that of obtaining formulations that are uniformly stable and convergent. Concrete examples are presented of element choices that lead to unstable formulations in the classical formulation, and which are stable for the formulations introduced here. A selection of numerical results illustrates in a comparative way the behaviour of the elements introduced.
The mathematical basis of FEMs for incompressible steady interior flow
problems is examined in a text (a revised and expanded version of the
work of Girault and Raviart, 1979) intended for a postgraduate course in
numerical analysis. Chapters are devoted to the mathematical foundation
of the Stokes problem, results obtained with a standard FEM
approximation, the numerical solution of the Stokes problem in primitive
variables, incompressible mixed FEMs for solving the Stokes problem, and
the theory and approximation of the Navier-Stokes problem.
Three a posteriori error estimators for PEERS and BDMS elements in linear elasticity are presented: one residual error estimator and two estimators based on the solution of auxiliary local problems with different boundary conditions. All of them are reliable and efficient with respect to the standard norm and furthermore robust for nearly incompressible materials.
Traducción de: Finete Elemente Incluye bibliografía e índice