74 citations · 238 across the 21 of their papers we have counts for
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math.NA2013
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…
math.NA2013
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…
math.NA2013
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…