Arbitrary Order Mixed Mimetic Finite Differences Method with Nodal Degrees of Freedom

[摘要] In this work we consider a modification to an arbitrary order mixed mimetic finite difference method (MFD) for a diffusion equation on general polygonal meshes [1]. The modification is based on moving some degrees of freedom (DoF) for a flux variable from edges to vertices. We showed that for a non-degenerate element this transformation is locally equivalent, i.e. there is a one-to-one map between the new and the old DoF. Globally, on the other hand, this transformation leads to a reduction of the total number of degrees of freedom (by up to 40%) and additional continuity of the discrete flux.

[发布日期] 2016-09-01

[学科分类] 数学（综合）

[关键词] Mathematics;mimetic finite difference;mixed diffusion