In this paper, we are concerned with a kind of Signorinitransmission problem in a unbounded domain. A variationalinequality is derived when discretizing this problem by coupledFEM-BEM. To solve such variational inequality, an iterativemethod, which can be viewed as a variant of the D-N alternativemethod, will be introduced. In the iterative method, the finiteelement part and the boundary element part can be solvedindependently. It will be shown that the convergence speed of thisiteration is independent of the mesh size. Besides, a combinationbetween this method and the steepest descent method is alsodiscussed.

Using systematically a tricky idea of N.V. Krylov, we obtain general results on the rate of convergence of a certain class of monotone approximation schemes for stationary Hamilton-Jacobi-Bellman equations with variable coefficients. This result applies in particular to control schemes based on the dynamic programming principle and to finite difference schemes despite, here, we are not able to treat the most general case. General results have been obtained earlier by Krylov for finite difference schemes in the stationary case with constant coefficients and in the time-dependent case with variable coefficients by using control theory and probabilistic methods. In this paper we are able to handle variable coefficients by a purely analytical method. In our opinion this way is far simpler and, for the cases we can treat, it yields a better rate of convergence than Krylov obtains in the variable coefficients case.

We study a finite volume method, used to approximate the solution of the linear two dimensional convection diffusion equation, with mixed Dirichlet and Neumann boundary conditions, on Cartesian meshes refined by an automatic technique (which leads to meshes with hanging nodes). We propose an analysis through a discrete variational approach, in a discrete H 1 finite volume space. We actually prove the convergence of the scheme in a discrete H 1 norm, with an error estimate of order O(h) (on meshes of size h).