74 citations · 238 across the 21 of their papers we have counts for
21 papers
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…
Self-propulsion dynamics of small droplets on general surfaces with curvature gradient
Yujuan Chen, Xianmin Xu
We study theoretically the self-propulsion dynamics of a small droplet on general curved surfaces by a variational approach. A new reduced model is derived based on careful computa…
Effective boundary conditions for dynamic contact angle hysteresis on chemically inhomogeneous surfaces
Zhen Zhang, Xianmin XU
Recent experiments (Guan et al. 2016a,b) showed many interesting phenomena on dynamic contact angle hysteresis while there is still a lack of complete theoretical interpretation. I…
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…
Theoretical analysis for dynamic contact angle hysteresis on chemically patterned surfaces
Xianmin Xu, Xiaoping Wang
A dynamic wetting problem is studied for a moving thin fiber inserted in fluid and with a chemically inhomogeneous surface. A reduced model is derived for contact angle hysteresis…
Theoretical analysis for flattening of a rising bubble in a Hele-Shaw cell
Xianmin Xu, Masao Doi, Jiajia Zhou +1
We calculate the shape and the velocity of a bubble rising in an infinitely large and closed Hele-Shaw cell using Park and Homsy's boundary condition which accounts for the change…
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…
Power-law scaling for solid-state dewetting of thin films: an Onsager variational approach
Wei Jiang, Xianmin Xu, Weizhu Bao +1
We examine the kinetics of surface diffusion-controlled, solid-state dewetting by consideration of the retraction of the contact in a semi-infinite solid thin film on a flat rigid…
Application of Onsager Machlup integral in solving dynamic equations in non-equilibrium systems
Masao Doi, Jiajia Zhou, Yana Di +1
In 1931, Onsager proposed a variational principle which has become the base of many kinetic equations for non-equilibrium systems. We have been showing that this principle is usefu…
Sharp-interface limits of a phase-field model with a generalized Navier slip boundary condition for moving contact lines
Xianmin Xu, Yana Di, Haijun Yu
The sharp-interface limits of a phase-field model with a generalized Navier slip boundary condition for moving contact line problem are studied by asymptotic analysis and numerical…
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…
Modified Wenzel and Cassie equations for wetting on rough surfaces
Xianmin Xu
We study a stationary wetting problem on rough and inhomogeneous solid surfaces. We derive a new formula for the apparent contact angle by asymptotic two-scale homogenization metho…
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…
Volterra-composition operators on the weighted Bergman space with exponential type weights
Xiaohua Pan, Yan Wu, Xianmin Xu
The properties of Volterra-composition operators on the weighted Bergman space with exponential type weights are investigated in this paper. We state some necessary and sufficient…
Finite element methods for a class of continuum models for immiscible flows with moving contact lines
A. Reusken, X. Xu, L. Zhang
In this paper we present a finite element method (FEM) for two-phase incompressible flows with moving contact lines. We use a sharp interface Navier-Stokes model for the bulk phase…
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…