High Order $$C^0$$C0-Continuous Galerkin Schemes for High Order PDEs, Conservation of Quadratic Invariants and Application to the Korteweg-de Vries Model
High Order $$C^0$$C0-Continuous Galerkin Schemes for High Order PDEs, Conservation of Quadratic Invariants and Application to the Korteweg-de Vries Model
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DOI：
10.1007/s10915-017-0455-2
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发表时间：
2018
影响因子：
2.5
通讯作者：
S. Minjeaud;R. Pasquetti
中科院分区：
文献类型：
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作者：
S. Minjeaud;R. Pasquetti
我们将 Korteweg-de Vries 方程视为一个有趣的高阶偏微分方程模型，并表明，在（唯一）共形伽辽金近似（即谱元法）的基础上，在准确性、计算效率、实施简单性以及（如果需要）较低不变量的守恒方面，可以开发出可靠且有效的方案。所提出的方法可以优先扩展到其他偏微分方程和多维问题。
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)-conformal Galerkin approximation, namely the Spectral Element Method. The proposed approach isa priorieasily extensible to other partial differential equations and to multidimensional problems.