2 research outputs found
bounds for numerical solutions of noncoercive convection-diffusion equations
International audienceIn this work, we apply an iterative energy method à la de Giorgi in order to establish bounds for numerical solutions of noncoercive convection-diffusion equations with mixed Dirichlet-Neumann boundary conditions
A mixed finite volume scheme for anisotropic diffusion problems on any grid
We present a new finite volume scheme for anisotropic heterogeneous diffusion
problems on unstructured irregular grids, which simultaneously gives an
approximation of the solution and of its gradient. In the case of simplicial
meshes, the approximate solution is shown to converge to the continuous ones as
the size of the mesh tends to 0, and an error estimate is given. In the general
case, we propose a slightly modified scheme for which we again prove the
convergence, and give an error estimate. An easy implementation method is then
proposed, and the efficiency of the scheme is shown on various types of grids