Error analysis of a fictitious domain method applied to a Dirichlet problem

Vivette Girault1, Roland Glowinski1
1Laboratoire d’Analyse Numérique-Tour 55-65 5ème étage, Université Pierre et Marie Curie, Paris Cedex 05, France

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A. Agouzal, Analyse Numérique de Méthodes de Décomposition de Domaines. Méthodes de Domaines Fictifs avec Multiplicateurs de Lagrange. Thèse de Doctorat, Université de Pau, 1993.

A.K. Aziz and I. Babuška, Survey lectures on the mathematical foundations of the finite element method. The Mathematical Foundations of the Finite Element Method with Applications to Partial Differential Equations (ed. A.K. Aziz), Academic Press, 1972.

I. Babuška, The finite element method with Lagrange multipliers. Numer. Math.,20 (1973), 179–192.

I. Babuška, J.K. Lee and J.T. Oden, Mixed-hybrid finite element approximations of second-order elliptic boundary value problem. Comput. Methods Appl. Mech. Engrg.,11 (1977), 175–206.

F. Brezzi, On the existence, uniqueness and approximation of saddle-point problems arising from Lagrange multipliers. RAIRO Anal. Numér.,8 (1974), 129–151.

F. Brezzi and M. Fortin, Mixed and Hybrid Finite Element Methods. Springer-Verlag, 1991.

P.-G. Ciarlet, The Finite Element Method for Elliptic Problems. North-Holland, 1977.

P. Clément, Approximation by finite element functions using local regularization. RAIRO Anal. Numér.,9 (1975), 77–84.

M. Fortin, An analysis of the convergence of mixed finite element methods. RAIRO Anal. Numér.,11 (1977), 341–354.

V. Girault and P.-A. Raviart, Finite Element Methods for the Navier-Stokes Equations. SCM5, Springer-Verlag, 1986.

R. Glowinski, T. Pan and J. Périaux, A fictitious domain method for Dirichlet problem and applications. Comput. Methods Appl. Mech. Engrg.,111 (1994), 283–303.

R. Glowinski, T. Pan and J. Périaux, A fictitious domain method for external incompressible viscous flow modeled by Navier-Stokes equations. Comput. Methods Appl. Mech. Engrg.,112 (1994), 133–148.

P. Grisvard, Elliptic Problems in Nonsmooth Domains. Monographs and Studies in Mathematics24, Pitman, 1985.

J.-L. Lions and E. Magenes, Problèmes aux Limites Non Homogènes et Applications. Dunod, 1968.

J. Pitkäranta, Boundary subspaces for the finite element method with Lagrange multipliers. Numer. Math.,33 (1979), 273–289.

A.H. Schatz and L.B. Wahlbin, Maximum norm estimates in the finite element method on plane polygonal domains. Part 1. Math. Comp.,33 (1978), 73–109.

L.B. Wahlbin, Local behavior in finite element methods. Handbook of Numerical Analysis (eds. P.-G. Ciarlet and J.-L. Lions), North-Holland, 1991.