136 citations · 588 across the 51 of their papers we have counts for
8 papers · 1 filter
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…