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
