A mixed finite element method for nonlinear elasticity: two-fold saddle point approach and a-posteriori error estimate |
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Authors: | Mauricio A Barrientos Gabriel N Gatica Ernst P Stephan |
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Institution: | GI2MA, Departamento de Ingeniería Matemática, Universidad de Concepción, Casilla 160-C, Concepción, Chile; e-mail: {mbarrien/ggatica}@ing-mat.udec.cl, CL Institut für Angewandte Mathematik, Universit?t Hannover, Welfengarten 1, 30167 Hannover, Germany; e-mail: stephan@ifam.uni-hannover.de, DE
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Abstract: | Summary. We extend the applicability of stable mixed finite elements for linear plane elasticity, such as PEERS, to a mixed variational
formulation of hyperelasticity. The present approach is based on the introduction of the strain tensor as a further unknown,
which yields a two-fold saddle point nonlinear operator equation for the corresponding weak formulation. We provide the uniqueness of solution for the continuous and discrete
schemes, and derive the usual Cea estimate for the associated error. Finally, a reliable a-posteriori error estimate, based
on the solution of local Dirichlet problems, and well suited for adaptive computations, is also given.
Received August 5, 2000 / Published online August 17, 2001 |
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Keywords: | Mathematics Subject Classification (1991): 65N15 65N30 65J15 74B20 |
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