Pre-Publicación 2012-07
Ana I. Garralda Guillem, Gabriel N. Gatica, Antonio Marquez, Manuel Ruiz Galan:
A posteriori error analysis of twofold saddle point variational formulations for nonlinear boundary value problems
Abstract:
In this paper we recast the analysis of twofold saddle point variational formulations for several nonlinear boundary value problems arising in continuum mechanics, and derive reliable and efficient residual-based a posteriori error estimators for the associated Galerkin schemes. We illustrate the main results with nonlinear elliptic equations modelling heat conduction and hyperelasticity. The main tools of our analysis include a global inf-sup condition for a linearization of the problem, Helmholtz decompositions, local approximation properties of the Raviart-Thomas and Clement interpolation operators, inverse inequalities, and the localization technique based on triangle-bubble and edge-bubble functions. Finally, several numerical results confirming the theoretical properties of the estimator and showing the behaviour of the associated adaptive algorithms, are provided.
Esta prepublicacion dio origen a la(s) siguiente(s) publicación(es) definitiva(s):
Ana I. GARRALDA GUILLEM, Gabriel N. GATICA, Antonio MARQUEZ, Manuel RUIZ GALAN: A posteriori error analysis of twofold saddle point variational formulations for nonlinear boundary value problems. IMA Journal of Numerical Analysis, vol. 34, 1, pp. 326-361, (2014).