Numerical Method for Dirichlet Problem with Degeneration of the Solution on the Entire Boundary
by
Viktor A. Rukavishnikov *,† and Elena I. Rukavishnikova †
Viktor A. Rukavishnikov *,† and Elena I. Rukavishnikova †
Computing Center of Far-Eastern Branch, Russian Academy of Sciences, Kim-Yu-Chen Str. 65, Khabarovsk 680000, Russia
*
Author to whom correspondence should be addressed.
†
These authors contributed equally to this work.
Symmetry 2019, 11(12), 1455; https://doi.org/10.3390/sym11121455
Received: 10 November 2019 / Revised: 22 November 2019 / Accepted: 23 November 2019 / Published: 26 November 2019
(This article belongs to the Special Issue Mesh Methods - Numerical Analysis and Experiments)
The finite element method (FEM) with a special graded mesh is constructed for the Dirichlet boundary value problem with degeneration of the solution on the entire boundary of the two-dimensional domain. A comparative numerical analysis is performed for the proposed method and the classical finite element method for a set of model problems in symmetric domain. Experimental confirmation of theoretical estimates of accuracy is obtained and conclusions are made.
Keywords:
boundary value problems with degeneration of the solution on entire boundary of the domain; the method of finite elements; special graded mesh
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MDPI and ACS Style
Rukavishnikov, V.A.; Rukavishnikova, E.I. Numerical Method for Dirichlet Problem with Degeneration of the Solution on the Entire Boundary. Symmetry 2019, 11, 1455.
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