International Workshop on Reliable Methods of Mathematical Modelling Zurich , 6 - 8 July 2005 Christine Bernardi

Most often, in the discretization of a partial differential equation, one or several intermediate non-discrete problems appear between the continuous and discrete ones. In this case, the discretization is called multi-step. Let us quote timedependent equations where the intermediate problem is the time semi-discrete problem and the equations where a stabilization term is added befor the discretization in order to enhance the convergence. This means that several discretization parameters are involved and, in order to optimize the choice of each of them, several families of error indicators must be introduced. We presnet an example to explain however a posteriori estimates can be obtained in this case, the aim being to uncouple as much as possible the errors issued from the different steps.