Continuous metrics and mesh adaptation

This paper addresses the problem of finding the mesh representing at best in Lp a twice continuous differentiable function defined on the plane. A continuous setting of this problem is used. It relies on an abstract mesh model, the “continuous metrics” allowing a variational analysis and on the identification of an optimum. Anisotropic optimal meshes can then be specified. An extension to discontinuities is proposed. It involves the prediction of the convergence order of the underlying mesh adaptation method. We present a few numerical illustrations related to numerical solution representation and to image compression.