Derivation and Analysis of Piecewise Constant Conservative Approximation for Anisotropic Diffusion Problems

A variational approach to derive a piecewise constant conservative approximation of anisotropic diffusion equations is presented. A priori error estimates are derived assuming usual mesh regularity constraints and a posteriori error indicator is proposed and analyzed for the model problem

Nonlinear parabolic inequalities on a general convex domain

International audienceThe paper deals with the existence and uniqueness of solutions of some non linear parabolic inequalities in the Orlicz-Sobolev spaces framework

A posteriori error estimates for non conforming approximation of quasi Stokes problem

International audienceWe derive and analyze an a posteriori error estimator for nonconforming finite element approximation for the quasi-Stokes problem, which is based on the solution of local problem on stars with low cost computation, this indicator is equivalent to the energy error norm up to data oscillation, neither saturation assumption nor comparison with residual estimator are made

Edge-based a Posteriori Error Estimators for Generating Quasi-optimal Simplicial Meshes

We present a new method for generating a d-dimensional simplicial mesh that minimizes the Lp-norm, p > 0, of the interpolation error or its gradient. The method uses edge-based error estimates to build a tensor metric. We describe and analyze the basic steps of our metho

A Posteriori Error Estimates on Stars for Convection Diffusion Problem

In this paper, a new a posteriori error estimator for nonconforming convection diffusion approximation problem, which relies on the small discrete problems solution in stars, has been established. It is equivalent to the energy error up to data oscillation without any saturation assumption nor comparison with residual estimato

A numerical method for waste repository problems with non-standard interface condition.

International audienc

Stability of reaction fronts in thin domains

The paper is devoted to the stability of reaction fronts in thin domains. The influence of natural convection and of heat losses through the walls of the reactor is studied numerically and analytically. Critical conditions of stability of stationary solutions are obtained