136 citations · 588 across the 51 of their papers we have counts for
64 papers
Surface Stokes-Cahn-Hilliard System: Analysis and Structure-Preserving Discretization
Maxim Olshanskii, Mansur Shakipov
We study the surface Stokes-Cahn-Hilliard system governing tangential flow and phase separation in viscous fluid membranes. The equations are posed on a closed, stationary hy…
Convergence of a CutFEM for fluid--structure interaction with a deforming interface
Miguel A. Fernández, Buyang Li, Maxim A. Olshanskii
We present a rigorous error analysis for a semidiscrete immersed CutFEM applied to fluid--structure interaction (FSI) problems involving an incompressible viscous fluid and an elas…
Well-posedness of the heat equation in domains with topological transitions
Maxim Olshanskii, Arnold Reusken
We analyze a linear parabolic equation with homogeneous Dirichlet boundary conditions posed in domains whose evolution may involve topological transitions. The domains are describe…
Analysis of a finite element method for PDEs in evolving domains with topological changes
Maxim A. Olshanskii, Arnold Reusken
The paper presents the first rigorous error analysis of an unfitted finite element method for a linear parabolic problem posed on an evolving domain that may undergo a topol…
Model order reduction of parametric dynamical systems by slice sampling tensor completion
Alexander V. Mamonov, Maxim A. Olshanskii
Recent studies have demonstrated the great potential of reduced order modeling for parametric dynamical systems using low-rank tensor decompositions (LRTD). In particular, within t…
Approximating a branch of solutions to the Navier--Stokes equations by reduced-order modeling
Maxim A. Olshanskii, Leo G. Rebholz
This paper extends a low-rank tensor decomposition (LRTD) reduced order model (ROM) methodology to simulate viscous flows and in particular to predict a smooth branch of solutions…
A priori analysis of a tensor ROM for parameter dependent parabolic problems
Alexander V. Mamonov, Maxim A. Olshanskii
A space-time-parameters structure of parametric parabolic PDEs motivates the application of tensor methods to define reduced order models (ROMs). Within a tensor-based ROM framewor…
An adaptive stabilized trace finite element method for surface PDEs
Timo Heister, Maxim A. Olshanskii, Vladimir Yushutin
The paper introduces an adaptive version of the stabilized Trace Finite Element Method (TraceFEM) designed to solve low-regularity elliptic problems on level-set surfaces using a s…
Local conservation laws of continuous Galerkin method for the incompressible Navier--Stokes equations in EMAC form
Maxim A. Olshanskii, Leo G. Rebholz
We consider local balances of momentum and angular momentum for the incompressible Navier-Stokes equations. First, we formulate new weak forms of the physical balances (conservatio…
An Eulerian finite element method for the linearized Navier--Stokes problem in an evolving domain
Michael Neilan, Maxim Olshanskii
The paper addresses an error analysis of an Eulerian finite element method used for solving a linearized Navier--Stokes problem in a time-dependent domain. In this study, the domai…
A scalar auxiliary variable unfitted FEM for the surface Cahn-Hilliard equation
Maxim Olshanskii, Yerbol Palzhanov, Annalisa Quaini
The paper studies a scalar auxiliary variable (SAV) method to solve the Cahn-Hilliard equation with degenerate mobility posed on a smooth closed surface Γ. The SAV formulation is c…
On equilibrium states of fluid membranes
Maxim A. Olshanskii
The paper studies the equilibrium configurations of inextensible elastic membranes exhibiting lateral fluidity. Using a continuum description of the membrane's motions based on the…
Tensorial parametric model order reduction of nonlinear dynamical systems
Alexander V. Mamonov, Maxim A. Olshanskii
For a nonlinear dynamical system that depends on parameters, the paper introduces a novel tensorial reduced-order model (TROM). The reduced model is projection-based, and for syste…
An Eulerian finite element method for tangential Navier-Stokes equations on evolving surfaces
Maxim A. Olshanskii, Arnold Reusken, Paul Schwering
The paper introduces a geometrically unfitted finite element method for the numerical solution of the tangential Navier--Stokes equations posed on a passively evolving smooth close…
Tangential Navier-Stokes equations on evolving surfaces: Analysis and simulations
Maxim A. Olshanskii, Arnold Reusken, Alexander Zhiliakov
The paper considers a system of equations that models a lateral flow of a Boussinesq--Scriven fluid on a passively evolving surface embedded in . For the resulting Na…
Lipid domain coarsening and fluidity in multicomponent lipid vesicles: A continuum based model and its experimental validation
Y. Wang, Y. Palzhanov, A. Quaini +2
Liposomes that achieve a heterogeneous and spatially organized surface through phase separation have been recognized to be a promising platform for delivery purposes. However, thei…
Interpolatory tensorial reduced order models for parametric dynamical systems
Alexander V. Mamonov, Maxim A. Olshanskii
The paper introduces a reduced order model (ROM) for numerical integration of a dynamical system which depends on multiple parameters. The ROM is a projection of the dynamical syst…
A comparison of Cahn-Hilliard and Navier-Stokes-Cahn-Hilliard models on manifolds
Maxim Olshanskii, Yerbol Palzhanov, Annalisa Quaini
We consider phase-field models with and without lateral flow for the numerical simulation of lateral phase separation and coarsening in lipid membranes. For the numerical solution…
A CutFEM divergence-free discretization for the Stokes problem
Haoran Liu, Michael Neilan, Maxim Olshanskii
We construct and analyze a CutFEM discretization for the Stokes problem based on the Scott-Vogelius pair. The discrete piecewise polynomial spaces are defined on macro-element tria…
A finite element method for two-phase flow with material viscous interface
Maxim Olshanskii, Annalisa Quaini, Qi Sun
This paper studies a model of two-phase flow with an immersed material viscous interface and a finite element method for numerical solution of the resulting system of PDEs. The int…
A monolithic fluid-porous structure interaction finite element method
Alexander Lozovskiy, Maxim A. Olshanskii, Yuri V. Vassilevski
The paper introduces a fully discrete quasi-Lagrangian finite element method for a monolithic formulation of a fluid-porous structure interaction problem. The method is second orde…
A decoupled, stable, and linear FEM for a phase-field model of variable density two-phase incompressible surface flow
Yerbol Palzhanov, Alexander Zhiliakov, Annalisa Quaini +1
The paper considers a thermodynamically consistent phase-field model of a two-phase flow of incompressible viscous fluids. The model allows for a non-linear dependence of fluid den…
An unfitted finite element method for two-phase Stokes problems with slip between phases
Maxim Olshanskii, Annalisa Quaini, Qi Sun
We present an isoparametric unfitted finite element approach of the CutFEM or Nitsche-XFEM family for the simulation of two-phase Stokes problems with slip between phases. For the…
Recycling augmented Lagrangian preconditioner in an incompressible fluid solver
Maxim Olshanskii, Alexander Zhiliakov
The paper discusses a reuse of matrix factorization as a building block in the Augmented Lagrangian (AL) and modified AL preconditioners for non-symmetric saddle point linear algeb…