Abstract
The problem of finding the best mesh in a numerical simulation is addressed with the introduction of a scalar output and of an adjoint state in combination with an a priori error model. This strategy is organised around a continuous modelling of mesh description and numerical error. The mesh description is done by the specification of a continuous metric. This is a scalar field defining the mesh fineness over the domain. A truncation error is modelled from an a priori estimate in function of the metric. The numerical error is then derived from the truncation error using a "state system" having the truncation error as right hand side. This allows to formulate the optimal mesh problem under the form of a continuous Optimal Control problem, with a control, the metric, a state equation, the error equation, and a functional, the error on scalar output. The minimisation with respect to the metric is applied under a control constraint expressing the fact that the equivalent mesh has a specified number of nodes. Examples dealing with elliptic model problems will be presented. The optimisation process is implemented with a gradient method and produce the optimal metric. Then an adapted mesh is generated. This process is reiterated a few times.