Author(s):
Isaev Vadim Ismailovitch
Position: Student
Address: 630090, Russia, Novosibirsk
Phone Office: (383) 330 73 46
E-mail: issaev.vadim@gmail.com

Shapeev Vasily Pavlovich
Dr. , Professor
Position: General Scientist
Office: Institute of Theoretical and Applied Mechanics of SB RAS, Novosibirsk State University
Address: 630090, Russia, Novosibirsk, Institutskaya Str., 4/1
Phone Office: (383) 330 27 13
E-mail: vshapeev@ngs.ru
SPIN-code: 7128-5536

Idimeshev Semyon Vasilyevich
Position: Junior Research Scientist
Office: Federal Research Center for Information and Computational Technologies
Address: 630090, Russia, Novosibirsk, Akademika Rzhanova ave., 6
Phone Office: (383)330-93-61
E-mail: idimeshev@gmail.com
SPIN-code: 3793-6120

References:
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[2] Shapeev, A. V., Shapeev, V. P. High-order accurate difference schemes for elliptic equations in a domain with a curvilinear boundary. Computational Mathematics and Mathematical Physics. 2000; 40(2):213-221.
[3] Botella, O., Peyret, R. Benchmark spectral results on the lid-driven cavity flow. Computers & Fluids. 1998; 27(4):421–433.
[4] Shapeev, A.V., Lin, P. An asymptotic fitting finite element method with exponential mesh refinement for accurate computation of corner eddies in viscous flows. SIAM Journal on Scientific Computing. 2009; 31(3):1874–1900.
[5] Sleptsov, A.G. Collocation-grid solution of elliptic boundary-value problems. Modelirovanie v mekhanike. 1991; 5(22(2)):101–126. (In Russ.)
[6] Isaev, V.I., Shapeev, V.P. High-accuracy versions of the collocations and least squares method for the numerical solution of the Navier–Stokes equations. Computational Mathematics and Mathematical Physics. 2010; 50(10):1670–1681.
[7] Gibou, F., Fedkiw, R. A fourth order accurate discretization for the Laplace and heat equations on arbitrary domains, with applications to the Stefan problem. Journal of Chemical Physics. 2005; 202 (2):577-601.
[8] Xu-Dong, Liu, Fedkiw, R., Myungjoo Kang. A Boundary Condition Capturing Method for Poisson’s Equation on Irregular Domains. Journal of Chemical Physics. 2000; 160 (1):151-178.
[9] Sleptsov, A.G., Shokin, Yu. I. An adaptiv grid-projection method for elliptic problems. Computational Mathematics and Mathematical Physics. 1997; 37(5):558–571.
[10] Beljaev, V. V., Shapeev, V. P.. The collocation and least squares method on adaptiv grids in a domain with a curvilinear boundary. Computational Technologies. 2000; 5(4):12–21. (In Russ.)
[11] Golushko, S.K., Idimeshev, S.V., Shapeev, V.P. Application of collocations and least residuals method to problems of the isotropic plates theory. Computational Technologies. 2013; 18(6), P. 31–43. (In Russ.)
[12] Semin, L.G., Sleptsov, A.G., Shapeev, V.P. Method of collocations - least squares for Stokes equations. Computational Technologies. 1996; 1(2):90–98. (In Russ.)
[13] Isaev, V. I., Shapeev, V. P. Development of the collocations and least squares method. Trudy Instituta Matematiki i Mekhaniki UrO RAN. 2008; 14(1):41-60. (In Russ.)
[14] Shapeev, V.P., Vorozhtsov, E.V., Isaev, V.I., Idimeshev, S.V. The method of collocations and least residuals for three-dimensional Navier-Stokes equations. Section 1. Numerical methods and applications. Numerical Methods and programming. 2013; 14(1):306-322. (In Russ.)
[15] Shapeev, V.P. Collocation and Least Residuals Method and Its Applications. EPJ Web of Conferences 108, 01009. 2016. DOI: 10.1051/epjconf/201610801009. Available at: http://www.epj-conferences.org/articles/epjconf/pdf/2016/03/epjconf_mmcp2016_01009.pdf
[16] Isaev, V.I., Shapeev, V.P., Eremin, S.A. An investigation of the collocation and the least squares method for solution of boundary value problems for the Navier-Stokes and Poisson equations. Computational Technologies. 2007; 12(3):53–70. (In Russ.)
[17] Sleptsov, A.G. On convergence acceleration of linear iterations II. Modelirovanie v mekhanike. 1989; 3(5):118–125. (In Russ.)
[18] Saad, Y. Numerical methods for large eigenvalue problems. Manchester University Press; 1991: 358.
[19] Timoshenko, S.P., Voynovskiy-Kriger, C. Plastiny i obolochki [Theory of Plates and Shells]. Moscow: Fizmatgiz; 1963: 536. ( In Russ.)