Computational free surfaces, non-Newtonian and high speed flows, unfitted finite element methods, numerical PDEs posed on surfaces and in a bulk, linear algebra tools in computational fluid dynamics.
Main publications:
M. A. Olshanskii, E. E. Tyrtyshnikov, Iterative Methods for Linear Systems: Theory and Applications, SIAM, 2014
M. Benzi, M. A. Olshanskii, Z. Wang, “Modified augmented Lagrangian preconditioners for the incompressible Navier–Stokes equations”, International Journal for Numerical Methods in Fluids, 66:4 (2011), 486–508
M. Benzi, M. A. Olshanskii, “An augmented Lagrangian-based approach to the Oseen problem”, SIAM Journal on Scientific Computing, 28:6 (2006), 2095–2113
T. Gelhard, G. Lube, M. A. Olshanskii, J. H. Starcke, “Stabilized finite element schemes with LBB-stable elements for incompressible flows”, Journal of Computational and Applied Mathematics, 177:2 (2005), 243–267
M. A. Olshanskii, A. Reusken, “Grad-div stablilization for Stokes equations”, Mathematics of Computation, 73:248 (2004), 1699–1718
P. P. Grinevich, M. A. Ol'shanskii, “An iterative method for solving the regularized Bingham problem”, Num. Meth. Prog., 11:1 (2010), 78–87
2004
2.
M. A. Ol'shanskii, “An analysis of the multigtrid method for the convection-diffusion equations with the Dirichlet boundary conditions”, Zh. Vychisl. Mat. Mat. Fiz., 44:8 (2004), 1450–1479; Comput. Math. Math. Phys., 44:8 (2004), 1374–1403
M. A. Ol'shanskii, E. V. Chizhonkov, “On the best constant in the inf-sup condition for elongated rectangular domains”, Mat. Zametki, 67:3 (2000), 387–396; Math. Notes, 67:3 (2000), 325–332
M. A. Ol'shanskii, “An exact numerical method for solving the Stokes-type factorized problem”, Zh. Vychisl. Mat. Mat. Fiz., 37:2 (1997), 202–213; Comput. Math. Math. Phys., 37:2 (1997), 198–209
1996
6.
M. A. Ol'shanskiĭ, “On a Stokes-type problem with a parameter”, Zh. Vychisl. Mat. Mat. Fiz., 36:2 (1996), 75–86; Comput. Math. Math. Phys., 36:2 (1996), 193–202
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