Publication Date:
2014-01-25
Description:
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's decompositions, local approximation properties of the Raviart–Thomas and Clément 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.
Print ISSN:
0272-4979
Electronic ISSN:
1464-3642
Topics:
Mathematics
