On the convergence on nonrectangular grids

The convergence properties of a full discrete approximations to the convection-diffusion equation is the subject of this paper. The full discrete scheme considered is of Lagrangian type: Euler Implicit on time and centered finite difference on space, and is defined using nonrectangular grids. We analyse this scheme under smoothness conditions on nonrectangular space-time grid. The main result establish the convergence of the approximations and we prove that the assumptions on the discrete spatial nodes movement are achieved if we consider the equidistribution principle.