Superconvergence of the Local Discontinuous Galerkin Method for Elliptic Problems on Cartesian Grids
Superconvergence of the Local Discontinuous Galerkin Method for Elliptic Problems on Cartesian Grids
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DOI：
10.1137/s0036142900371544
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发表时间：
2001
期刊：
影响因子：
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通讯作者：
Bernardo Cockburn;G. Kanschat;I. Perugia;D. Schötzau
中科院分区：
文献类型：
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作者：
Bernardo Cockburn;G. Kanschat;I. Perugia;D. Schötzau
在本文中，我们提出了一个局部间断Galerkin（LDG）方法的超收敛性结果的模型椭圆问题在笛卡尔网格。我们确定了一个特殊的数值通量的梯度和L2-范数的潜在的分别是k+1/2和k+1，当张量积多项式的次数最多为k，对于任意网格，这种特殊的LDG方法只给出了k和k+1/2，分别收敛的顺序。我们提出了一系列的数值例子，建立我们的理论结果的清晰度。
In this paper, we present a superconvergence result for the local discontinuous Galerkin (LDG) method for a model elliptic problem on Cartesian grids. We identify a special numerical flux for which the L2-norm of the gradient and the L2-norm of the potential are of orders k+1/2 and k+1, respectively, when tensor product polynomials of degree at most k are used; for arbitrary meshes, this special LDG method gives only the orders of convergence of k and k+1/2, respectively. We present a series of numerical examples which establish the sharpness of our theoretical results.