Journal of Mathematical Sciences

, Volume 150, Issue 2, pp 1998–2004 | Cite as

A finite element method for solving singular boundary-value problems

  • M. N. Yakovlev


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.


Russia Finite Element Method Mathematical Institute Steklov Mathematical Institute 
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  1. 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).MATHGoogle Scholar
  2. 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).MATHGoogle Scholar
  3. 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).MATHGoogle Scholar

Copyright information

© Springer Science+Business Media, Inc. 2008

Authors and Affiliations

  • M. N. Yakovlev
    • 1
  1. 1.St.Petersburg Department of the Steklov Mathematical InstituteSt.PetersburgRussia

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