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June  2005, 4(2): 267-281. doi: 10.3934/cpaa.2005.4.267

Approximations of degree zero in the Poisson problem

C. Davini 1, and  F. Jourdan 2,

1. 

Dipartimento di Georisorse e Territorio, University of Udine, 33100 Udine, Italy
2. 

LMGC, Université de Montpellier II, Montpellier, France

Received  April 2004 Revised  November 2004 Published  March 2005

We discuss a technique for the approximation of the Poisson problem under mixed boundary conditions in spaces of piece-wise constant functions. The method adopts ideas from the theory of $\Gamma$-convergence as a guideline. Some applications are considered and numerical evaluation of the convergence rate is discussed.
Keywords: non-conforming approximations, Γ-convergence, Poisson problem, Numerical methods.
Mathematics Subject Classification: 65N12,65N30,46N40,74K1.
Citation: C. Davini, F. Jourdan. Approximations of degree zero in the Poisson problem. Communications on Pure & Applied Analysis, 2005, 4 (2) : 267-281. doi: 10.3934/cpaa.2005.4.267
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