In the paper we introduce Rv–generalized solution to the Stokes problem with singularity in a non-convex polygonal domain with one reentrant corner on its boundary. The weighted analogue of the LBB condition is proved. A new weighted finite element method is constructed. Results of numerical experiments have shown the efficiency of the method.
REFERENCES
1.
H.
Blum
, “The influence of reentrant corners in the numerical approximation of viscous flow problems,” in Numerical Treatment of the Navier-Stokes Equations
, 30
(Springer
, 1990
).2.
3.
4.
V. A.
Rukavishnikov
, Doklady Mathematics
90
, 562
–564
(2014
).5.
V. A.
Rukavishnikov
and A. V.
Rukavishnikov
, Jour. of Comp. and Appl. Math.
341
, 144
–156
(2018
).6.
V. A.
Rukavishnikov
and H. I.
Rukavishnikova
, Jour. of Comp. and Appl. Math.
234
, 2870
–2882
(2010
).7.
V. A.
Rukavishnikov
and A. O.
Mosolapov
, Jour. of Comp. Phys.
231
, 2438
–2448
(2012
).8.
V. A.
Rukavishnikov
and H. I.
Rukavishnikova
, Numer. Func. Anal. and Optimization
34
, 1328
–1347
(2013
).9.
V. A.
Rukavishnikov
and A. O.
Mosolapov
, Doklady Mathematics
87
, 156
–159
(2013
).10.
V. A.
Rukavishnikov
and S. G.
Nikolaev
, Doklady Mathematics
88
, 705
–709
(2013
).11.
V. A.
Rukavishnikov
and A. V.
Rukavishnikov
, Bulletin SUSU MMCS
11
, 95
–108
(2018
).12.
L. R.
Scott
and M.
Vogelius
, Math. Model. and Numer. Anal.
19
, 111
–143
(1985
).
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