On the Properties of Operators of the Stokes Problem with Corner Singularity in Nonsymmetric Variational Formulation

Viktor A. Rukavishnikov and Alexey V. Rukavishnikov
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Viktor A. Rukavishnikov: Computing Center of the Far Eastern Branch of the Russian Academy of Sciences, Kim Yu Chen Str. 65, 680000 Khabarovsk, Russia
Alexey V. Rukavishnikov: Institute of Applied Mathematics of the Far Eastern Branch of the Russian Academy of Sciences, Dzerzhinsky Str. 54, 680000 Khabarovsk, Russia

Mathematics, 2022, vol. 10, issue 6, 1-32

Abstract: The weighted finite element method makes it possible to find an approximate solution of a boundary value problem with corner singularity without loss of accuracy. The construction of this numerical method is based on the introduction of the concept of an R ν -generalized solution for a boundary value problem with a singularity. In this paper, special weighted sets based on the corresponding operators from the definition of the R ν -generalized solution of the Stokes problem in a nonsymmetric variational formulation are introduced. The properties and relationships of these weighted sets are established.

Keywords: stokes problem; corner singularity; R ? -generalized solution (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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