Sibirskii Zhurnal Vychislitel'noi Matematiki
 RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
 General information Latest issue Archive Impact factor Subscription Search papers Search references RSS Latest issue Current issues Archive issues What is RSS

 Sib. Zh. Vychisl. Mat.: Year: Volume: Issue: Page: Find

 Sib. Zh. Vychisl. Mat., 2001, Volume 4, Number 3, Pages 201–228 (Mi sjvm396)

The use of singular functions in the $h$-$p$ version of the finite element method for a Dirichlet problem with degeneration of the input data

A. Yu. Bespalov, V. A. Rukavishnikov

Computing Center, Far-Eastern Branch, Russian Academy of Sciences, Khabarovsk, Russia

Abstract: The paper is devoted to a Dirichlet problem for a second-order non-self-adjoint elliptic equation with a strong singularity of the solution caused by a coordinated degeneration of input data at boundary points of a two-dimensional domain. The h-p version of the finite element method is used to approximate this problem. We introduce a finite element space with a singular basis that depends on the space to which the solution to the problem belongs. An exponential convergence rate in the norm of a weighted Sobolev space is proved.

Full text: PDF file (1331 kB)
References: PDF file   HTML file

Bibliographic databases:
UDC: 519.632
Language:

Citation: A. Yu. Bespalov, V. A. Rukavishnikov, “The use of singular functions in the $h$-$p$ version of the finite element method for a Dirichlet problem with degeneration of the input data”, Sib. Zh. Vychisl. Mat., 4:3 (2001), 201–228

Citation in format AMSBIB
\Bibitem{BesRuk01}
\by A.~Yu.~Bespalov, V.~A.~Rukavishnikov
\paper The use of singular functions in the $h$-$p$ version of the finite element method for a Dirichlet problem with degeneration of the input data
\jour Sib. Zh. Vychisl. Mat.
\yr 2001
\vol 4
\issue 3
\pages 201--228
\mathnet{http://mi.mathnet.ru/sjvm396}
\zmath{https://zbmath.org/?q=an:0987.65118}

• http://mi.mathnet.ru/eng/sjvm396
• http://mi.mathnet.ru/eng/sjvm/v4/i3/p201

 SHARE:

Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
1. Bespalov A., “Orthogonal Systems of Singular Functions and Numerical Treatment of Problems with Degeneration of Data”, Adv. Comput. Math., 19:1-3 (2003), 159–182
2. E. V. Kashuba, V. A. Rukavishnikov, “On the $p$-version of the finite element method for the boundary value problem with singularity”, Sib. zhurn. vychisl. matem., 8:1 (2005), 31–42
3. Rukavishnikov V.A., Kuznetsova E.V., “Coercive estimate for a boundary value problem with noncoordinated degeneration of the data”, Differ. Equ., 43:4 (2007), 550–560
4. Arroyo D., Bespalov A., Heuer N., “On the Finite Element Method for Elliptic Problems with Degenerate and Singular Coefficients”, Math. Comput., 76:258 (2007), 509–537
5. V. A. Rukavishnikov, E. V. Kuznetsova, “A scheme of a finite element method for boundary value problems with non-coordinated degeneration of input data”, Num. Anal. Appl., 2:3 (2009), 250–259
6. Rukavishnikov V.A., “Methods of Numerical Analysis for Boundary Value Problems with Strong Singularity”, Russ. J. Numer. Anal. Math. Model, 24:6 (2009), 565–590
•  Number of views: This page: 215 Full text: 75 References: 25