52 citations · 134 across the 11 of their papers we have counts for
13 papers
A finite element discretization with semi-implicit nonlinear multistep scheme for a two-dimensional competition-diffusion system of three competing species with different mobility rates
Xianping Li, Woinshet D. Mergia, Kailash C. Patidar
In ecological studies of pattern formation, models of the competitive-diffusion type are generally singularly perturbed, and the numerical approximation of such models is challengi…
Moving Mesh with Streamline Upwind Petrov-Galerkin (MM-SUPG) Method for Time-dependent Convection-Dominated Convection-Diffusion Problems
Xianping Li, Matthew McCoy
Time-dependent convection-dominated convection-diffusion problems are considered. We develop a moving mesh streamline upwind Petrov-Galerkin (MM-SUPG) method by combining residual-…
A Preliminary Comparison Between Compressive Sampling and Anisotropic Mesh-based Image Representation
Xianping Li, Teresa Wu
Compressed sensing (CS) has become a popular field in the last two decades to represent and reconstruct a sparse signal with much fewer samples than the signal itself. Although reg…
Anisotropic Mesh Adaptation for Image Segmentation Based on Mumford-Shah Functional
Karrar Abbas, Xianping Li
As the resolution of digital images increase significantly, the processing of images becomes more challenging in terms of accuracy and efficiency. In this paper, we consider image…
A Study on Phase-Field Models for Brittle Fracture
Fei Zhang, Weizhang Huang, Xianping Li +1
In the phase-field modeling of brittle fracture, anisotropic constitutive assumptions for the degradation of stored elastic energy due to fracture are crucial to preventing crackin…
Anisotropic Mesh Adaptation for Finite Element Solution of Anisotropic Porous Medium Equation
Xianping Li
Anisotropic Porous Medium Equation (APME) is developed as an extension of the Porous Medium Equation (PME) for anisotropic porous media. A special analytical solution is derived fo…
Moving mesh finite element simulation for phase-field modeling of brittle fracture and convergence of newton's iteration
Fei Zhang, Weizhang Huang, Xianping Li +1
A moving mesh finite element method is studied for the numerical solution of a phase-field model for brittle fracture. The moving mesh partial differential equation approach is emp…
A study on nonnegativity preservation in finite element approximation of Nagumo-type nonlinear differential equations
Xianping Li, Weizhang Huang
Preservation of nonnengativity and boundedness in the finite element solution of Nagumo-type equations with general anisotropic diffusion is studied. Linear finite elements and the…
Anisotropic mesh adaptation for 3D anisotropic diffusion problems with application to fractured reservoir simulation
Xianping Li, Weizhang Huang
Anisotropic mesh adaptation is studied for linear finite element solution of 3D anisotropic diffusion problems. The M-uniform mesh approach is used, where an anisotropic adaptive m…
Anisotropic Mesh Adaptation for Image Representation
Xianping Li
Triangular meshes have gained much interest in image representation and have been widely used in image processing. This paper introduces a framework of anisotropic mesh adaptation…
Maximum principle for the finite element solution of time dependent anisotropic diffusion problems
Xianping Li, Weizhang Huang
Preservation of the maximum principle is studied for the combination of the linear finite element method in space and the -method in time for solving time dependent anisotropic…
Anisotropic Mesh Adaptation for Variational Problems Using Error Estimation Based on Hierarchical Bases
Weizhang Huang, Lennard Kamenski, Xianping Li
Anisotropic mesh adaptation has been successfully applied to the numerical solution of partial differential equations but little considered for variational problems. In this paper,…
An anisotropic mesh adaptation method for the finite element solution of heterogeneous anisotropic diffusion problems
Xianping Li, Weizhang Huang
Heterogeneous anisotropic diffusion problems arise in the various areas of science and engineering including plasma physics, petroleum engineering, and image processing. Standard n…