Mimetic finite difference method for the stokes problem on polygonal meshes

Thumbnail image of item number 1 in: 'Mimetic finite difference method for the stokes problem on polygonal meshes'.
Thumbnail image of item number 2 in: 'Mimetic finite difference method for the stokes problem on polygonal meshes'.
Thumbnail image of item number 3 in: 'Mimetic finite difference method for the stokes problem on polygonal meshes'.
Thumbnail image of item number 4 in: 'Mimetic finite difference method for the stokes problem on polygonal meshes'.
Showing 1-4 of 23 pages in this article.

PDF Version Also Available for Download.

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.

Context

This article is part of the collection entitled: Office of Scientific & Technical Information Technical Reports and was provided by UNT Libraries Government Documents Department to Digital Library, a digital repository hosted by the UNT Libraries. More information about this article can be viewed below.

Who

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

Authors

Sponsor

Publisher

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.

About | Browse this Partner

Contact Us

Corrections Questions

What

Descriptive information to help identify this article. Follow the links below to find similar items on the Digital Library.

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

Language

Item Type

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
  • Archival Resource Key: ark:/67531/metadc930059

Collections

This article is part of the following collection of related materials.

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.

About | Browse this Collection

What responsibilities do I have when using this article?

Digital Files

When

Dates and time periods associated with this article.

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

When was this article last used?

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

Interact With This Article

Here are some suggestions for what to do next.

Start Reading

Thumbnail image of item number 1 in: 'Mimetic finite difference method for the stokes problem on polygonal meshes'.
Thumbnail image of item number 2 in: 'Mimetic finite difference method for the stokes problem on polygonal meshes'.
Thumbnail image of item number 3 in: 'Mimetic finite difference method for the stokes problem on polygonal meshes'.
Thumbnail image of item number 4 in: 'Mimetic finite difference method for the stokes problem on polygonal meshes'.

PDF Version Also Available for Download.

Citations, Rights, Re-Use

International Image Interoperability Framework

IIF Logo

We support the IIIF Presentation API

Lipnikov, K; Beirao Da Veiga, L; Gyrya, V & Manzini, G. Mimetic finite difference method for the stokes problem on polygonal meshes, article, January 1, 2009; [New Mexico]. (digital.library.unt.edu/ark:/67531/metadc930059/: accessed January 15, 2019), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.