The mimetic finite difference discretization of diffusion problem on unstructured polyhedral meshes
The mimetic finite difference discretization of diffusion problem on unstructured polyhedral meshes
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DOI：
10.1016/j.jcp.2005.05.028
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发表时间：
2006-01
影响因子：
4.1
通讯作者：
K. Lipnikov;M. Shashkov;D. Svyatskiy
中科院分区：
文献类型：
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作者：
K. Lipnikov;M. Shashkov;D. Svyatskiy
研究了扩散型问题在非结构多面体网格上的拟有限差分离散。我们证明了高精度的近似解一般扩散张量，二阶收敛速度的标量未知和一阶收敛速度的矢量未知光滑或稍微扭曲的网格上，非匹配网格，甚至网格上的不规则形状的多面体与平面。我们表明，在一般情况下，网格与非平面需要一个以上的通量未知每个网格面，以获得最佳的收敛速度。
We study the mimetic finite difference discretization of diffusion-type problems on unstructured polyhedral meshes. We demonstrate high accuracy of the approximate solutions for general diffusion tensors, the second-order convergence rate for the scalar unknown and the first order convergence rate for the vector unknown on smooth or slightly distorted meshes, on non-matching meshes, and even on meshes with irregular-shaped polyhedra with flat faces. We show that in general the meshes with non-flat faces require more than one flux unknown per mesh face to get optimal convergence rates.