Approximations of degree zero in the Poisson problem

Authors :: C. Davini
Franck Jourdan
Couplages en Géomécanique et Biomécanique (CGB)
Laboratoire de Mécanique et Génie Civil (LMGC)
Université de Montpellier (UM)-Centre National de la Recherche Scientifique (CNRS)-Université de Montpellier (UM)-Centre National de la Recherche Scientifique (CNRS)
Source :: Communications on Pure and Applied Analysis, Communications on Pure and Applied Analysis, AIMS American Institute of Mathematical Sciences, 2005, 4 (2), pp.269-283. ⟨10.3934/cpaa.2005.4.267⟩
Publication Year :: 2005
Publisher :: American Institute of Mathematical Sciences (AIMS), 2005.
Abstract: 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.