# High Order $C^0$-Continuous Galerkin Schemes for High Order PDEs, Conservation of Quadratic Invariants and Application to the Korteweg-de Vries Model

2 CASTOR - Control, Analysis and Simulations for TOkamak Research
CRISAM - Inria Sophia Antipolis - Méditerranée
Abstract : We address the Korteweg-de Vries equation as an interesting model of high order partial differential equation, and 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 the lower invariants, on the basis of a (only) $H^1$-conformal Galerkin approximation, namely the Spectral Element Method. The proposed approach is {\it a priori} easily extensible to other partial differential equations and to multidimensional problems.
Keywords :
Document type :
Journal articles
Complete list of metadatas

Cited literature [58 references]

https://hal.archives-ouvertes.fr/hal-01158007
Contributor : Sebastian Minjeaud <>
Submitted on : Tuesday, November 5, 2019 - 11:43:47 AM
Last modification on : Wednesday, December 4, 2019 - 3:17:03 PM
Long-term archiving on: Friday, February 7, 2020 - 9:41:34 AM

### File

MP_16_FINAL_HAL.pdf
Files produced by the author(s)

### Citation

Sebastian Minjeaud, Richard Pasquetti. High Order $C^0$-Continuous Galerkin Schemes for High Order PDEs, Conservation of Quadratic Invariants and Application to the Korteweg-de Vries Model. Journal of Scientific Computing, Springer Verlag, 2018, 74 (1), pp.491-518. ⟨10.1007/s10915-017-0455-2⟩. ⟨hal-01158007v2⟩

Record views