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A finite element method for solving singular boundary-value problems

Authors:

M. N. Yakovlev

Affiliation:

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

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

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

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

Keywords:

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