74 citations · 238 across the 21 of their papers we have counts for
11 papers · 1 filter
A Geometrically Consistent Trace Finite Element Method For The Laplace-Beltrami Eigenvalue Problem
Song Lu, Xianmin Xu
In this paper, we propose a new trace finite element method for the {Laplace-Beltrami} eigenvalue problem. The method is proposed directly on a smooth manifold which is implicitly…
A variational analysis for the moving finite element method for gradient flows
Xianmin Xu
By using the Onsager principle as an approximation tool, we give a novel derivation for the moving finite element method for gradient flow equations. We show that the discretized p…
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…
An efficient diffusion generated motion method for wetting dynamics
Song Lu, Xianmin Xu
By using the Onsager variational principle as an approximation tool, we develop a new diffusion generated motion method for wetting problems. The method uses a signed distance func…
A stabilized trace finite element method for partial differential equations on evolving surfaces
Christoph Lehrenfeld, Maxim A. Olshanskii, Xianmin Xu
In this paper, we study a numerical method for the solution of partial differential equations on evolving surfaces. The numerical method is built on the stabilized trace finite ele…
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…
An efficient threshold dynamics method for wetting on rough surfaces
Xianmin Xu, Dong Wang, Xiaoping Wang
The threshold dynamics method developed by Merriman, Bence and Osher (MBO) is an efficient method for simulating the motion by mean curvature flow when the interface is away from t…
A multiscale finite element method for oscillating Neumann problem on rough domain
P. B. Ming, X. Xu
We develop a new multiscale finite element method for Laplace equation with oscillating Neumann boundary conditions on rough boundaries. The key point is the introduction of a new…
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…
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…