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Existence result and discontinuous finite element discretization for a plane stresses Hencky problem
Author(s) -
Dhia H. Ben,
Hadhri T.,
Nedelec J. C.
Publication year - 1989
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.1670110202
Subject(s) - mathematics , discretization , finite element method , convergence (economics) , subsequence , plane (geometry) , weak convergence , element (criminal law) , mathematical analysis , mathematical optimization , geometry , computer science , physics , computer security , political science , law , economics , bounded function , asset (computer security) , thermodynamics , economic growth
We hereafter propose and analyse a discontinuous finite element method for a plane stress Hencky problem. For that purpose we begin by proving an existence result for the continuous problem. A kind of Green's formula between\documentclass{article}\pagestyle{empty}\begin{document}$$ BD\left(\Omega \right) = \left\{{u \in {\rm{L}}^1 \left(\Omega \right),\varepsilon _{ij} (u) \in M_1 \left(\Omega \right)} \right\}{\rm{and}}H\left(\Omega \right) = \left\{{\sigma \in L^\infty \left(\Omega \right),div\sigma \in {\rm{L}}^2 \left(\Omega \right)} \right\} $$\end{document} and other intermediate results that may be of independent interest are presented and established separately. Then we formulate the discretized problem, give an existence result for it and prove a result of weak convergence of a subsequence of discrete solutions to a solution of the continuous problem.