High order \(C^0\)-continuous Galerkin schemes for high order PDEs, conservation of quadratic invariants and application to the Korteweg-de Vries model
This paper deals with solutions of the Korteweg-de Vries equation and focus on development of reliable and effective schemes. Particularly, the accuracy, computational efficiency, simplicity of implementation of the scheme is investigated as well as the possible conservation of the lower invariants. The considered schemes are derived on the basis of a \(H^1\)-conformal Galerkin approximation, namely, the spectral element method. The theoretical results are supported by numerical results.
scientific article; zbMATH DE number 6845865
scientific article