Analysis of a mixed finite-volume discretization of fourth-order equations on general surfaces
Analysis of a mixed finite-volume discretization of fourth-order equations on general surfaces
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DOI：
10.1093/imanum/drn021
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发表时间：
2008-04
影响因子：
2.1
通讯作者：
Q. Du;L. Ju;Li Tian
中科院分区：
文献类型：
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作者：
Q. Du;L. Ju;Li Tian
本文研究了一个定义在光滑曲面上的四阶偏微分方程模型的有限体积方法。离散化是通过一个表面网格组成的分段平面三角形和它的对偶表面多边形镶嵌。给出了一般正则网格上近似解在H1-范数下的误差估计.在不同的样品表面上进行了数值实验，以验证理论结果。此外，当底层网格是由所谓的约束质心Voronoi网格，我们提出了一个数值证明的超收敛计划，更准确地计算梯度。
In this paper, we study a finite-volume method for the numerical solution of a model fourth-order partial differential equation defined on a smooth surface. The discretization is done via a surface mesh consisting of piecewise planar triangles and its dual surface polygonal tessellation. We provide an error estimate for the approximate solution under the H 1 -norm on general regular meshes. Numerical experiments are carried out on various sample surfaces to verify the theoretical results. In addition, when the underlying mesh is constructed by the so-called constrained centroidal Voronoi meshes, we propose a numerically demonstrated superconvergent scheme to compute gradients more accurately.