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## Section: New Results

### Spectral Element method for high order partial differential equations

Participants : Sebastian Minjeaud, Richard Pasquetti.

The Korteweg-de Vries equation has been addressed as an interesting model of high order partial differential equation. In [9] it is shown that it is possible to develop reliable and effective schemes, in terms of accuracy, computational efficiency, simplicity of implementation and, if required, conservation of the lower invariants, on the basis of a (only) ${H}^{1}$-conformal Galerkin approximation, namely the Spectral Element Method. The proposed approach is a priori easily extensible to other partial differential equations and to multidimensional problems.