Convergence of Finite Volume MPFA O type Schemes for Heterogeneous Anisotropic Diffusion Problems on General Meshes
Convergence of Finite Volume MPFA O type Schemes for Heterogeneous Anisotropic Diffusion Problems on General Meshes
复制标题
一般网格上非均质各向异性扩散问题的有限体积MPFA O型方案的收敛性
DOI：
--
复制
发表时间：
2010
期刊：
影响因子：
--
通讯作者：
R. Masson
中科院分区：
文献类型：
--
作者：
L. Agélas;Cindy Guichard;R. Masson
本文证明了各向异性和非均质扩散问题的有限体积多点通量近似（MPFA） O格式的收敛性。我们的框架是基于一个离散的混合变分公式，它推广了MPFA O方案的通常结构。在局部矫顽力条件下，导出了该格式的适定性和收敛性，该条件易于数值验证。我们的框架的新颖之处在于它适用于一般多边形和多面体网格以及$L^{\infty}$扩散系数，这在许多实际应用中是必不可少的。
In this paper we prove the convergence of the finite volume MultiPoint Flux Approximation (MPFA) O scheme for anisotropic and heterogeneous diffusion problems. Our framework is based on a discrete hybrid variational formulation which generalizes the usual construction of the MPFA O scheme. The well-posedness and convergence of the scheme is derived assuming a local coercivity condition which can be easily checked numerically. The novel feature of our framework is that it holds for general polygonal and polyhedral meshes as well as for $L^{\infty}$ diffusion coefficients, which is essential in many practical applications.