Finite volume approximation of a class of variational inequalities (Q2725339)

The authors prove convergence results for the approximate finite volume solution of a diffusion problem with mixed Dirichlet, Neumann and Signorini boundary conditions which is formulated as a variational inequality of the form NEWLINE\[NEWLINE\int_\Omega \nabla u(x)\cdot \nabla(v-u)(x)dx\geq\int_{\Gamma^3} b(\gamma(v)-\gamma(u))(s)ds,\quad \forall v\in K,NEWLINE\]NEWLINE where NEWLINE\[NEWLINEu\in K=\{v\in H^1(\Omega),\;v|_{\Gamma^1}=0,\;v|_{\Gamma^3}\geq 0\;\text{a.e.}\}NEWLINE\]NEWLINE An error estimate of order one with respect to the mesh size is given when the solutions to the continuous problems belong to \(H^2(\Omega)\).