136 citations · 588 across the 51 of their papers we have counts for
5 papers · 2 filters
Trace Finite Element Methods for PDEs on Surfaces
Maxim A. Olshanskii, Arnold Reusken
In this paper we consider a class of unfitted finite element methods for discretization of partial differential equations on surfaces. In this class of methods known as the Trace F…
A trace finite element method for PDEs on evolving surfaces
Maxim A. Olshanskii, Xianmin Xu
In this paper, we propose an approach for solving PDEs on evolving surfaces using a combination of the trace finite element method and a fast marching method. The numerical approac…
On conservation laws of Navier-Stokes Galerkin discretizations
Sergey Charnyi, Timo Heister, Maxim A. Olshanskii +1
We study conservation properties of Galerkin methods for the incompressible Navier-Stokes equations, without the divergence constraint strongly enforced. In typical discretizations…
Inf-sup stability of geometrically unfitted Stokes finite elements
Johnny Guzmán, Maxim Olshanskii
The paper shows an inf-sup stability property for several well-known 2D and 3D Stokes elements on triangulations which are not fitted to a given smooth or polygonal domain. The pro…
Numerical integration over implicitly defined domains for higher order unfitted finite element methods
Maxim Olshanskii, Danil Safin
The paper studies several approaches to numerical integration over a domain defined implicitly by an indicator function such as the level set function. The integration methods are…