This article is cited 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

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.

UDC: 519.632

Received: 30.11.2000

Language: English

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