136 citations · 588 across the 51 of their papers we have counts for
6 papers · 1 filter
An Eulerian space-time finite element method for diffusion problems on evolving surfaces
Maxim A. Olshanskii, Arnold Reusken, Xianmin Xu
In this paper, we study numerical methods for the solution of partial differential equations on evolving surfaces. The evolving hypersurface in defines a -dimensiona…
A connection between filter stabilization and eddy viscosity models
Maxim A. Olshanskii, Xin Xiong
Recently, a new approach for the stabilization of the incompressible Navier-Stokes equations for higher Reynolds numbers was introduced based on the nonlinear differential filterin…
Non-degenerate Eulerian finite element method for solving PDEs on surfaces
Alexey Y. Chernyshenko, Maxim A. Olshanskii
The paper studies a method for solving elliptic partial differential equations posed on hypersurfaces in , . The method builds upon the formulation introduced…
A finite element solver and energy stable coupling for 3D and 1D fluid models
Tatiana K. Dobroserdova, Maxim A. Olshanskii
The paper develops a solver based on a conforming finite element method for a 3D--1D coupled incompressible flow problem. New coupling conditions are introduced to ensure a suitabl…
On surface meshes induced by level set functions
Maxim A. Olshanskii, Arnold Reusken, Xianmin Xu
The zero level set of a piecewise-affine function with respect to a consistent tetrahedral subdivision of a domain in is a piecewise-planar hyper-surface. We prove t…
A stabilized finite element method for advection-diffusion equations on surfaces
Maxim A. Olshanskii, Arnold Reusken, Xianmin Xu
A recently developed Eulerian finite element method is applied to solve advection-diffusion equations posed on hypersurfaces. When transport processes on a surface dominate over di…