24 citations · 54 across the 6 of their papers we have counts for
6 papers
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…
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…
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…
Experimental validation of a phase-field model to predict coarsening dynamics of lipid domains in multicomponent membranes
Alexander Zhiliakov, Yifei Wang, Annalisa Quaini +2
Membrane phase-separation is a mechanism that biological membranes often use to locally concentrate specific lipid species in order to organize diverse membrane processes. Phase se…
Error analysis of higher order trace finite element methods for the surface Stokes equations
Thomas Jankuhn, Maxim A. Olshanskii, Arnold Reusken +1
The paper studies a higher order unfitted finite element method for the Stokes system posed on a surface in three-dimensional space. The method employs generalized Taylor-Hood fini…
Inf-sup stability of the trace P2-P1 Taylor-Hood elements for surface PDEs
Maxim A. Olshanskii, Arnold Reusken, Alexander Zhiliakov
The paper studies a geometrically unfitted finite element method (FEM), known as trace FEM or cut FEM, for the numerical solution of the Stokes system posed on a closed smooth surf…