A generalization of the vertex-centered finite volume scheme to arbitrary high order
A generalization of the vertex-centered finite volume scheme to arbitrary high order
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DOI：
10.1007/s00791-010-0139-z
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发表时间：
2010-06
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通讯作者：
A. Vogel;Jinchao Xu;G. Wittum
中科院分区：
文献类型：
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作者：
A. Vogel;Jinchao Xu;G. Wittum
提出了求解任意阶椭圆型问题的高阶有限体积法。采用分段多项式基函数作为试验函数，控制体采用顶点中心技术构造。利用二维三角形和四边形的数值实例对离散化进行了验证。在这些测试中，在h1范数中实现了最佳误差。2-范数的误差比偶数多项式次的最优值低一个阶，比奇数次的最优值低一个阶。
A higher order finite volume method for elliptic problems is proposed for arbitrary order. Piecewise polynomial basis functions are used as trial functions while the control volumes are constructed by a vertex-centered technique. The discretization is tested on numerical examples utilizing triangles and quadrilaterals in 2D. In these tests the optimal error is achieved in theH1-norm. The error in theL2-norm is one order below optimal for even polynomial degrees and optimal for odd degrees.