Existence result and discontinuous finite element discretization for a plane stresses Hencky problem

摘要

AbstractWe 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 betweendocumentclass{article}pagestyle{empty}begin{document}$$ BDleft(Omega right) = left{{u in {rm{L}}^1 left(Omega right),varepsilon _{ij} (u) in M_1 left(Omega right)} right}{rm{and}}Hleft(Omega right) = left{{sigma in L^infty left(Omega right),divsigma in {rm{L}}^2 left(Omega right)} right} $$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.