On an optimal finite element scheme for the advection equation

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• 作者：Argus A. Dunca ^{argus_dunca@yahoo.com" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Finite element methods ; Advection equation ; Differential filters
• 刊名：Journal of Computational and Applied Mathematics
• 出版年：2017
• 出版时间：February 2017
• 年：2017
• 卷：311
• 期：Complete
• 页码：522-528
• 全文大小：758 K

文摘

In this report it is presented a numerical finite element scheme for the advection equation that attains the optimal L²$L^2$ convergence rate O(h^k+1)$\mathcal{O}\left(h^{k+1}\right)$ when order k$k$ finite elements are used, improving the order O(h^k+0.5)$\mathcal{O}\left(h^{k+0.5}\right)$ of other previous regularization methods. This result is also confirmed by the numerical test performed in the last section. The scheme assumes unstructured grids, periodic boundary conditions, a constant advection field and a bit (two units) stronger regularity on the exact solution than in the classical (suboptimal) finite element theory.