一种应用于二维DG方法的次优策略

Serendipity square elements of high degree up to 10 times are constructed as a strategy for two dimensional applications of nodal DG methods. By pre-imposing the Legendre-Gauss-Lobatto (LGL) quadrature points on the borders to keep good interpolation properties and maintain boundary conforming characteristics, the novel construction method evolves a global-like solution of a constrained nonlinear optimization problem to maximize the absolute value of the Vandermonde determinant of the point set. The final point set with certain symmetry property produces low Lebesgue constants which indicate low interpolation errors, and the constants fall among the ranges of those of different point sets already known in literature. Compared with the constant metric elements equipped with nodal points of compact pattern, only two additional points are introduced for the newly presented strategy and that is also why the strategy is called suboptimal. On the other hand, the new strategy has a much smaller scale of nodal points than the traditional tensor product points, therefore it remarkably saves computing and storage resources and is more suitable for application.