This article is cited in 6 scientific papers (total in 6 papers)
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
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.
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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
\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.
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This publication is cited in the following articles:
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
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
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
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
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
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
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