# Mimetic finite difference method for the stokes problem on polygonal meshes

### Description

Various approaches to extend the finite element methods to non-traditional elements (pyramids, polyhedra, etc.) have been developed over the last decade. Building of basis functions for such elements is a challenging task and may require extensive geometry analysis. The mimetic finite difference (MFD) method has many similarities with low-order finite element methods. Both methods try to preserve fundamental properties of physical and mathematical models. The essential difference is that the MFD method uses only the surface representation of discrete unknowns to build stiffness and mass matrices. Since no extension inside the mesh element is required, practical implementation of the MFD ... continued below

### Creation Information

Lipnikov, K; Beirao Da Veiga, L; Gyrya, V & Manzini, G January 1, 2009.

## Who

People and organizations associated with either the creation of this article or its content.

### Provided By

#### UNT Libraries Government Documents Department

Serving as both a federal and a state depository library, the UNT Libraries Government Documents Department maintains millions of items in a variety of formats. The department is a member of the FDLP Content Partnerships Program and an Affiliated Archive of the National Archives.

## What

### Description

Various approaches to extend the finite element methods to non-traditional elements (pyramids, polyhedra, etc.) have been developed over the last decade. Building of basis functions for such elements is a challenging task and may require extensive geometry analysis. The mimetic finite difference (MFD) method has many similarities with low-order finite element methods. Both methods try to preserve fundamental properties of physical and mathematical models. The essential difference is that the MFD method uses only the surface representation of discrete unknowns to build stiffness and mass matrices. Since no extension inside the mesh element is required, practical implementation of the MFD method is simple for polygonal meshes that may include degenerate and non-convex elements. In this article, we develop a MFD method for the Stokes problem on arbitrary polygonal meshes. The method is constructed for tensor coefficients, which will allow to apply it to the linear elasticity problem. The numerical experiments show the second-order convergence for the velocity variable and the first-order for the pressure.

### Source

• Journal Name: Journal of Computational Physics

### Identifier

Unique identifying numbers for this article in the Digital Library or other systems.

• Report No.: LA-UR-09-00753
• Report No.: LA-UR-09-753
• Grant Number: AC52-06NA25396
• Office of Scientific & Technical Information Report Number: 956391

### Collections

#### Office of Scientific & Technical Information Technical Reports

Reports, articles and other documents harvested from the Office of Scientific and Technical Information.

Office of Scientific and Technical Information (OSTI) is the Department of Energy (DOE) office that collects, preserves, and disseminates DOE-sponsored research and development (R&D) results that are the outcomes of R&D projects or other funded activities at DOE labs and facilities nationwide and grantees at universities and other institutions.

## When

### Creation Date

• January 1, 2009

### Added to The UNT Digital Library

• Nov. 13, 2016, 7:26 p.m.

### Description Last Updated

• Dec. 12, 2016, 6:05 p.m.

### Usage Statistics

Yesterday: 0
Past 30 days: 0
Total Uses: 5

Here are some suggestions for what to do next.