An HDG Method with Orthogonal Projections in Facet Integrals
An HDG Method with Orthogonal Projections in Facet Integrals
复制标题
面积分中正交投影的 HDG 方法
DOI：
10.1007/s10915-018-0648-3
复制
发表时间：
2018
影响因子：
2.5
通讯作者：
Oikawa Issei
中科院分区：
文献类型：
--
作者：
Takahito Kashiwabara; Issei Oikawa;and Guanyu Zhou;Oikawa Issei
提出并分析了求解二阶椭圆问题的一种新的杂交间断Galerkin（HDG）方法。我们的方法是通过插入的正交投影到近似空间的数值跟踪到所有的面积分在通常的HDG制定。如果我们使用多项式的次数，和k，其中k和k是任何非负整数，来逼近向量，标量和跟踪变量，这意味着我们的方法可以实现超收敛的标量变量没有后处理的所有变量的收敛阶是最优的。数值结果验证了理论结果。
We propose and analyze a new hybridizable discontinuous Galerkin (HDG) method for second-order elliptic problems. Our method is obtained by inserting the-orthogonal projection onto the approximate space for a numerical trace into all facet integrals in the usual HDG formulation. The orders of convergence for all variables are optimal if we use polynomials of degree,andk, wherekandlare any non-negative integers, to approximate the vector, scalar and trace variables, which implies that our method can achieve superconvergence for the scalar variable without postprocessing. Numerical results are presented to verify the theoretical results.