Skip to main content
SpringerLink
Log in

A finite element method for solving singular boundary-value problems

  • Published:
Journal of Mathematical Sciences Aims and scope Submit manuscript

Abstract

It is proved that under certain assumptions on the functions q(t) and f(t), there is one and only one function u0(t) ∈ \(\mathop {W_2^1 }\limits^o (a,b)\) at which the functional

$$\int\limits_a^b {[u'(t)]^2 dt} + \int\limits_a^b {q(t)u^2 (t)dt} - 2\int\limits_a^b {f(t)u(t)dt} $$

attains its minimum. An error bound for the finite element method for computing the function u0(t) in terms of q(t), f(t), and the meshsize h is presented. Bibliography: 3 titles.

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. M. N. Yakovlev, “Solvability of singular boundary-value problems for ordinary differential equations of order 2m,” Zap. Nauchn. Semin. POMI, 309, 174–188 (2004).

    MATH  Google Scholar 

  2. M. N. Yakovlev, “Existence of nonnegative solutions of singular boundary-value for second-order ordinary differential equations,” Zap. Nauchn. Semin. POMI, 323, 215–222 (2005).

    MATH  Google Scholar 

  3. M. N. Yakovlev, “The first boundary-value problem for a singular nonlinear ordinary differential equation of fourth order,” Zap. Nauchn. Semin. POMI, 334, 233–245 (2006).

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. St.Petersburg Department of the Steklov Mathematical Institute, St.Petersburg, Russia

    M. N. Yakovlev

Authors
  1. M. N. Yakovlev
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

__________

Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 346, 2007, pp. 149–159.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Yakovlev, M.N. A finite element method for solving singular boundary-value problems. J Math Sci 150, 1998–2004 (2008). https://doi.org/10.1007/s10958-008-0115-z

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10958-008-0115-z

Keywords

Search

Navigation