Thesis Summary:

In this thesis we apply mixed—dual variational formulations to solve linear and nonlinear boundary value problems. More precisely, we are interested on dual-dual variational formulations, so called by the two—fold saddle point operator equations of the weak formulations. The main goal in this thesis is to realize an a-posteriori error analysis of these formulations. In fact, we develop two different a—posteriori error analyses yielding explicit residual and implicit Bank—Weiser type reliable estimates, respectively, for a linear exterior transmission problems in the plane. Several numerical results illustrate the suitability of these estimators for the adaptive computation of the discrete solutions. Next, a two—fold saddle point nonlinear operator equation is used in a mixed variational formulation of hyperelasticity. Also, a reliable a-posteriori error estimate, based on the solution of local Dirichlet problems, and well suited for adaptive computations, is also given. Finally, we follow the above ideas to solve a linear—nonlinear transmission problem in plane hyperelasticity with mixed boundary conditions, which yields a twofold saddle point operator equation as the corresponding variational formulation. We derive a reliable a-posteriori error estimate.

ISI Publications from the Thesis

Mauricio BARRIENTOS, Gabriel N. GATICA, Norbert HEUER: An a-posteriori error estimate for a linear-nonlinear transmission problem in plane elastostatics. Calcolo, vol. 39, 2, pp. 61-86, (2002)

Mauricio BARRIENTOS, Gabriel N. GATICA, Matthias MAISCHAK: A-posteriori error estimates for linear exterior problems via mixed-FEM and DtN mappings. Mathematical Modelling and Numerical Analysis, vol. 36, 2, pp. 241-272, (2002)

Mauricio BARRIENTOS, Gabriel N. GATICA, Ernst P. STEPHAN: A mixed finite element method for nonlinear elasticity: two-fold saddle approach and a-posteriori error estimate. Numerische Mathematik, vol. 91, 2, pp. 197-222, (2002)

Other Publications (ISI)

Mauricio BARRIENTOS, Gabriel N. GATICA, Rodolfo RODRíGUEZ, Marcela E. TORREJON: Analysis of a coupled BEM/FEM eigensolver for hydroelastic vibrations problems. Mathematical Modelling and Numerical Analysis, vol. 38, 4, pp. 653-672, (2004)

Gabriel R. BARRENECHEA, Mauricio BARRIENTOS, Gabriel N. GATICA: On the numerical analysis of finite element and Dirichlet-to-Neumann methods for nonlinear exterior transmission problems. Numerical Functional Analysis and Optimization, vol. 19, 7 & 8, pp. 705-735, (1998)