The L-stable second order single diagonal implicit Runge-Kutta method for finding a solution of nonlinear Navier-Stokes equations in rotation form in the L-shaped domain is applied. An Rν-generalized solution of the problem in weighted sets is defined. An unweighted finite element method is constructed to find its approximate solution. The results of numerical experiments have shown the advantage of the proposed method over the classical ones.

1.
V. A.
Rukavishnikov
and
E. I.
Rukavishnikova
,
Differ. Equ.
55
,
832
840
(
2019
).
2.
V. A.
Rukavishnikov
and
E. I.
Rukavishnikova
,
Mathematics
8
,
1870
(
2020
).
3.
V. A.
Rukavishnikov
,
A. O.
Mosolapov
, and
E. I.
Rukavishnikova
,
Comput. Struct.
243
,
106400
(
2021
).
4.
V. A.
Rukavishnikov
and
E. I.
Rukavishnikova
,
Symmetry
11
,
1455
(
2019
).
5.
V. A.
Rukavishnikov
and
O. P.
Tkachenko
,
Math. Meth. Appl. Sci.
43
,
7550
7568
(
2020
).
6.
V. A.
Rukavishnikov
and
E. I.
Rukavishnikova
,
J. Comput. Appl. Math.
403
,
113841
(
2022
).
7.
V. A.
Rukavishnikov
and
A. V.
Rukavishnikov
,
Bull. South Ural State Univ. Ser.: Math. Model. Program. Comput. Softw.
11
,
95
108
(
2018
).
8.
V. A.
Rukavishnikov
and
A. V.
Rukavishnikov
,
J. Comput. Appl. Math.
341
,
144
156
(
2018
).
9.
R.
Alexander
,
SIAM J. Numer. Anal.
14
,
1006
1021
(
1977
).
10.
V. A.
Rukavishnikov
and
A. V.
Rukavishnikov
,
Mathematics
10
(
6
),
889
(
2022
).
11.
A. V.
Rukavishnikov
and
V. A.
Rukavishnikov
,
Int. J. Comput. Methods
19
,
2250012
(
2022
).
12.
V. A.
Rukavishnikov
and
A. V.
Rukavishnikov
,
Mathematics
10
(
10
),
1752
(
2022
).
13.
J.
Qin
,
On the convergence of some low order mixed finite element for incompressible fluids
, Ph.D. thesis,
Pennsylvania State University
(
1994
).
14.
L. R.
Scott
and
M.
Vogelius
,
ESAIM: Math. Model. Numer. Anal.
19
,
111
143
(
1985
).
15.
V. A.
Rukavishnikov
and
A. V.
Rukavishnikov
,
Symmetry
11
,
54
(
2019
).
16.
V. A.
Rukavishnikov
and
A. V.
Rukavishnikov
,
Comput. Res. Model.
12
,
1291
1306
(
2020
).
17.
A. V.
Rukavishnikov
,
Comput. Contin. Mech.
15
,
19
30
(
2022
).
18.
A. V.
Rukavishnikov
,
J. Comput. Technol.
27
(
6
),
70
87
(
2022
).
19.
V. A.
Rukavishnikov
,
J. Appl. Comput. Mech.
7
,
2159
2170
(
2021
).
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