Section: New Results

Mesh adaptation for very high-order numerical scheme

Participants : Frédéric Alauzet [correspondant] , Adrien Loseille, Estelle Mbinky.

In the past, we have demonstrated that multi-scale anisotropic mesh adaptation is a powerful tool to accurately simulate compressible flow problems and to obtain faster convergence to continuous solutions. But, this was limited to second order numerical scheme. Nowadays, numerous teams are working on the development of very high-order numerical scheme (e.g. of third or greater order): Discontinous Galerkin, Residual Distribution scheme, Spectral method, ...

This work extend interpolation error estimates to higher order numerical solution representation. We have examined the case of third-order accuracy. The first step is to reduce the tri-linear form given by the third order error term into a quadratic form based on the third order derivative. From this local error model, the optimal mesh is exhibited thanks to the continuous mesh framework.