29 citations · 63 across the 10 of their papers we have counts for
13 papers
Practical tensor calculus on embedded submanifolds of arbitrary codimension
Vladimir Yushutin
We present a fully extrinsic, parametrization-free variant of tensor calculus on embedded, possibly evolving, submanifolds with boundary in arbitrary dimension and codimension. The…
Continuous data assimilation for problems with limited regularity using non-interpolant observables
Vladimir Yushutin
Continuous data assimilation addresses time-dependent problems with unknown initial conditions by incorporating observations of the solution into a nudging term. For the prototypic…
Inf-Sup Stability of Parabolic TraceFEM
Lucas Bouck, Ricardo H. Nochetto, Mansur Shakipov +1
We develop a parabolic inf-sup theory for a modified TraceFEM semi-discretization in space of the heat equation posed on a stationary surface embedded in . We conside…
A note on balance laws of coupled surface and bulk fluid flows
Qi Sun, Vladimir Yushutin
Balance laws of coupled bulk-surface-bulk fluid flows are considered. We carefully investigate how do the interface conditions influence the total mass, total momentum and total en…
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…
A hydrodynamical model of nematic liquid crystal films with a general state of orientational order
Lucas Bouck, Ricardo H. Nochetto, Vladimir Yushutin
We develop a Q-tensor model of nematic liquid crystals occupying a stationary surface which represents a fluidic material film in space. In addition to the evolution due to Landau-…
A finite element method for Allen-Cahn equation on deforming surface
Maxim Olshanskii, Xianmin Xu, Vladimir Yushutin
The paper studies an Allen-Cahn-type equation defined on a time-dependent surface as a model of phase separation with order-disorder transition in a thin material layer. By a forma…
Numerical modelling of phase separation on dynamic surfaces
Vladimir Yushutin, Annalisa Quaini, Maxim Olshanskii
The paper presents a model of lateral phase separation in a two component material surface. The resulting fourth order nonlinear PDE can be seen as a Cahn-Hilliard equation posed o…
On stability of Euler flows on closed surfaces of positive genus
Vladimir Yushutin
Incompressible flows of an ideal two-dimensional fluid on a closed orientable surface of positive genus are considered. Linear stability of harmonic, i.e. irrotational and incompre…
A computational study of lateral phase separation in biological membranes
Vladimir Yushutin, Annalisa Quaini, Sheereen Majd +1
Conservative and non-conservative phase-field models are considered for the numerical simulation of lateral phase separation and coarsening in biological membranes. An unfitted fin…
A penalty finite element method for a fluid system posed on embedded surface
Maxim A. Olshanskii, Vladimir Yushutin
The paper introduces a finite element method for the incompressible Navier--Stokes equations posed on a closed surface . The method needs a shape regular tetrahedra m…
A finite element method for the surface Stokes problem
Maxim A. Olshanskii, Annalisa Quaini, Arnold Reusken +1
We consider a Stokes problem posed on a 2D surface embedded in a 3D domain. The equations describe an equilibrium, area-preserving tangential flow of a viscous surface fluid and se…
Static stability of collapsible tube conveying non-Newtonian fluid
V. S. Yushutin
The global static stability of a Starling Resistor conveying non-Newtonian fluid is considered. The Starling Resistor consists of two rigid circular tubes and axisymmetric collapsi…