7 papers
A modified Brinkman penalization fictitious domain method for the unsteady Navier-Stokes equations
Zhanybek Baitulenov, Maxim Olshanskii, Almas Temirbekov +2
This paper investigates a modification of the fictitious domain method with continuation in the lower-order coefficients for the unsteady Navier-Stokes equations governing the moti…
Low-rank cross approximation of function-valued tensors for reduced-order modeling of parametric PDEs
Stanislav Budzinskiy, Vladimir Kazeev, Maxim Olshanskii
The paper considers function-valued tensors, viewed as multidimensional arrays with entries in an abstract Hilbert space. Despite the absence of the algebraic structure of a field,…
A Stabilized Trace FEM for Surface Cahn--Hilliard Equations: Analysis and Simulations
Deepika Garg, Maxim Olshanskii
This paper addresses the analysis and numerical assessment of a computational method for solving the Cahn--Hilliard equation defined on a surface. The proposed approach combines th…
An Augmented Lagrangian Preconditioner for Navier--Stokes Equations with Runge--Kutta in Time
Santolo Leveque, Yunhui He, Maxim Olshanskii
We consider a Runge--Kutta method for the numerical time integration of the nonstationary incompressible Navier--Stokes equations. This yields a sequence of nonlinear problems to b…
A parametric tensor ROM for the shallow water dam break problem
Md Rezwan Bin Mizan, Maxim Olshanskii, Ilya Timofeyev
We develop a variant of a tensor reduced-order model (tROM) for the parameterized shallow-water dam-break problem. This hyperbolic system presents multiple challenges for model red…
Projected gradient stabilization of sharp and diffuse interface formulations in unfitted Nitsche finite element methods
Maxim Olshanskii, Jan-Phillip Bäcker, Dmitri Kuzmin
We introduce an unfitted Nitsche finite element method with a new ghost-penalty stabilization based on local projection of the solution gradient. The proposed ghost-penalty operato…