Skip to main content
SpringerLink
Log in

P 0-approximation of \({\Delta(H_0^2 \cap W^{3,\infty})}\) on square grids based on interior squares

  • Original Paper
  • Area 1
  • Published:
Japan Journal of Industrial and Applied Mathematics Aims and scope Submit manuscript

Abstract

We will approximate a function in \({\Delta(H_0^2 \cap W^{3,\infty})}\) with a piecewise constant function on the square grids, whose degrees of freedom are based on the interior squares only. In spite of the slight lack of degrees of freedom, the approximation error is analyzed to be O(h) in L 2-norm, which is the optimal order for the piecewise-constant interpolation. The result in the paper is relevant to the finite element approximation for the divergence-free velocity in the Stokes problem with the locally divergence-free P 1-nonconforming space on the square grids.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Brezzi F., Fortin M.: Mixed and Hybrid Finite Element Methods. Springer, New York (1991)

    Book  MATH  Google Scholar 

  2. Gilbarg D., Trudinger N.S.: Elliptic Partial Differential Equations of Second Order. Springer, New York (1983)

    Book  MATH  Google Scholar 

  3. Girault V., Raviart P.A.: Finite Element Methods for the Navier–Stokes Equations: Theory and Algorithms. Springer, New York (1986)

    Book  MATH  Google Scholar 

  4. Park, C.: A study on locking phenomena in finite element methods. Ph.D. thesis, Department of mathematics, Seoul National University, Seoul, Korea (2002)

  5. Park C., Sheen D.: P 1-nonconforming quadrilateral finite element methods for second-order elliptic problems. SIAM J. Numer. Anal. 41, 624–640 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  6. Park, C.: P 1-nonconforming divergence-free finite element method on square grids for incompressible Stokes equations. http://home.konkuk.ac.kr/~cpark/divfreeStokes.pdf(to be submitted)

  7. Thomasset F.: Implementation of Finite Element Methods for Navier–Stokes Equations. Springer-Verlag, New York-Berlin (1981)

    Book  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Konkuk University, Seoul, 143-701, Korea

    Chunjae Park

Authors
  1. Chunjae Park
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Chunjae Park.

About this article

Cite this article

Park, C. P 0-approximation of \({\Delta(H_0^2 \cap W^{3,\infty})}\) on square grids based on interior squares. Japan J. Indust. Appl. Math. 30, 661–679 (2013). https://doi.org/10.1007/s13160-013-0121-5

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s13160-013-0121-5

Keywords

Mathematics Subject Classification

Search

Navigation