# 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:

- 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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