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Sibirskii Zhurnal Vychislitel'noi Matematiki, 2005, Volume 8, Number 1, Pages 31–42
(Mi sjvm208)
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This article is cited in 3 scientific papers (total in 3 papers)
On the $p$-version of the finite element method for the boundary value problem with singularity
E. V. Kashuba, V. A. Rukavishnikov Computer Centre Far-Eastern Branch of RAS
Abstract:
The one-dimensional first-type boundary value problem for the second order differential equation with strong singularity of a solution caused by coordinated degeneration of input data at the origin is considered. For this problem we define the solution as $R_{\nu}$-generalized one. It has been proved that solution belongs to the weighted Sobolev space $H^3_{2,\nu+\beta/2+1}$ under proper assumptions for coefficients and the right-hand side of the differential equation. The scheme of the finite element method is constructed on a fixed mesh using polynomials of an arbitrary degree $p$ (the $p$-version of the finite element method). The finite element space contains singular polynomials. Using the regularity of $R_{\nu}$-generalized solution, the estimate for the rate of convergence of the second order with respect to the degree $p$ of polynomials is proved in the norm of the weighted Sobolev space.
Key words:
the $p$-version of the finite element method, boundary value problems with singularity, the weighted Sobolev spaces, an orthonormalized singular polynomials set.
Received: 03.11.2003 Revised: 31.05.2004
Citation:
E. V. Kashuba, V. A. Rukavishnikov, “On the $p$-version of the finite element method for the boundary value problem with singularity”, Sib. Zh. Vychisl. Mat., 8:1 (2005), 31–42
Linking options:
https://www.mathnet.ru/eng/sjvm208 https://www.mathnet.ru/eng/sjvm/v8/i1/p31
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Abstract page: | 285 | Full-text PDF : | 89 | References: | 52 |
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