Section: New Results

High order $C^0$-continuous Galerkin schemes for high order PDEs

Participants : Sebastian Minjeaud, Richard Pasquetti.

We show that it is possible to develop reliable and effective schemes, in terms of accuracy, computational efficiency, simplicity of implementation and, if required, conservation of linear or quadratic invariants, for high order partial differential equation on the basis of a (only) $H^1$-conformal Galerkin approximation, namely the Spectral Element Method. We address the Korteweg-de Vries equation but the proposed approach is a priori easily extensible to other partial differential equations and to multidimensional problems.