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

Abstract

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.

Authors:
 [1];  [1];  [1]
  1. Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
Publication Date:
Research Org.:
Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
Sponsoring Org.:
USDOE National Nuclear Security Administration (NNSA)
OSTI Identifier:
1321697
Report Number(s):
LA-UR-16-26696
DOE Contract Number:  
AC52-06NA25396
Resource Type:
Technical Report
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICS AND COMPUTING; Mathematics; mimetic finite difference, mixed diffusion

Citation Formats

Iaroshenko, Oleksandr, Gyrya, Vitaliy, and Manzini, Gianmarco. Arbitrary Order Mixed Mimetic Finite Differences Method with Nodal Degrees of Freedom. United States: N. p., 2016. Web. doi:10.2172/1321697.
Iaroshenko, Oleksandr, Gyrya, Vitaliy, & Manzini, Gianmarco. Arbitrary Order Mixed Mimetic Finite Differences Method with Nodal Degrees of Freedom. United States. doi:10.2172/1321697.
Iaroshenko, Oleksandr, Gyrya, Vitaliy, and Manzini, Gianmarco. Thu . "Arbitrary Order Mixed Mimetic Finite Differences Method with Nodal Degrees of Freedom". United States. doi:10.2172/1321697. https://www.osti.gov/servlets/purl/1321697.
@article{osti_1321697,
title = {Arbitrary Order Mixed Mimetic Finite Differences Method with Nodal Degrees of Freedom},
author = {Iaroshenko, Oleksandr and Gyrya, Vitaliy and Manzini, Gianmarco},
abstractNote = {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.},
doi = {10.2172/1321697},
journal = {},
number = ,
volume = ,
place = {United States},
year = {Thu Sep 01 00:00:00 EDT 2016},
month = {Thu Sep 01 00:00:00 EDT 2016}
}

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