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

Iaroshenko, Oleksandr¹  Gyrya, Vitaliy¹  Manzini, Gianmarco¹ 

[1] Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

关键词: Mathematics;    mimetic finite difference;    mixed diffusion;   

DOI  :  10.2172/1321697
RP-ID  :  LA-UR--16-26696
PID  :  OSTI ID: 1321697

学科分类：数学（综合）

美国|英语

来源: SciTech Connect

【 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.