An augmented mixed finite element method with Lagrange multipliers: A priori and a posteriori error analyses

Barrios, TP; Gatica, GN

Abstract

In this paper, we provide a priori and a posteriori error analyses of an augmented mixed finite element method with Lagrange multipliers applied to elliptic equations in divergence form with mixed boundary conditions. The augmented scheme is obtained by including the Galerkin least-squares terms arising from the constitutive and equilibrium equations. We use the classical Babuška-Brezzi theory to show that the resulting dual-mixed variational formulation and its Galerkin scheme defined with Raviart-Thomas spaces are well posed, and also to derive the corresponding a priori error estimates and rates of convergence. Then, we develop a reliable and efficient residual-based a posteriori error estimate and a reliable and quasi-efficient Ritz projection-based one, as well. Finally, several numerical results illustrating the performance of the augmented scheme and the associated adaptive algorithms are reported. © 2006 Elsevier B.V. All rights reserved.

Más información

Título según WOS: An augmented mixed finite element method with Lagrange multipliers: A priori and a posteriori error analyses
Título según SCOPUS: An augmented mixed finite element method with Lagrange multipliers: A priori and a posteriori error analyses
Título de la Revista: JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
Volumen: 200
Número: 2
Editorial: ELSEVIER SCIENCE BV
Fecha de publicación: 2007
Página de inicio: 653
Página final: 676
Idioma: English
URL: http://linkinghub.elsevier.com/retrieve/pii/S0377042706000422
DOI:

10.1016/j.cam.2006.01.017

Notas: ISI, SCOPUS