13 citations · 21 across the 11 of their papers we have counts for
11 papers
Numerical integration rules with improved accuracy close to singularities
Sergio Amat, Zhilin Li, Juan Ruiz-Alvarez +2
Sometimes it is necessary to obtain a numerical integration using only discretised data. In some cases, the data contains singularities which position is known but does not coincid…
High order two-grid finite difference methods for interface and internal layer problems
Zhilin Li, Kejia Pan, Juan Ruiz
Second order accurate Cartesian grid methods have been well developed for interface problems in the literature. However, it is challenging to develop third or higher order accurate…
High order compact schemes for flux type BCs
Zhilin Li, Kejia Pan
In this paper new innovative fourth order compact schemes for Robin and Neumann boundary conditions have been developed for boundary value problems of elliptic PDEs in two and thre…
A simple third order compact finite element method for 1D BVP
Baiying Dong, Zhilin Li
A simple third order compact finite element method is proposed for one-dimensional Sturm-Liouville boundary value problems. The key idea is based on the interpolation error estimat…
Convergence study of IB methods for Stokes equations with no-slip boundary conditions
Zhilin Li, Kejia Pan, Juan Ruiz-Álvarez
Peskin's Immersed Boundary (IB) model and method are among one of the most important modeling tools and numerical methods. The IB method has been known to be first order accurate i…
An immersed - element for Stokes interface problems and the optimal convergence analysis
Haifeng Ji, Feng Wang, Jinru Chen +1
This paper presents and analyzes an immersed finite element (IFE) method for solving Stokes interface problems with a piecewise constant viscosity coefficient that has a jump acros…
Analysis of nonconforming IFE methods and a new scheme for elliptic interface problems
Haifeng Ji, Feng Wang, Jinru Chen +1
In this paper, an important discovery has been found for nonconforming immersed finite element (IFE) methods using the integral values on edges as degrees of freedom for solving el…
A new parameter free partially penalized immersed finite element and the optimal convergence analysis
Haifeng Ji, Feng Wang, Jinru Chen +1
This paper presents a new parameter free partially penalized immersed finite element method and convergence analysis for solving second order elliptic interface problems. A lifting…
On jump relations of anisotropic elliptic interface problems
Baiying Dong, Xiufang Feng, Zhilin Li
Almost all materials are anisotropic. In this paper, interface relations of anisotropic elliptic partial differential equations involving discontinuities across interfaces are deri…
Accurate gradient computations at interfaces using finite element methods
Fangfang Qin, Zhaohui Wang, Zhijie Ma +1
New finite element methods are proposed for elliptic interface problems in one and two dimensions. The main motivation is not only to get an accurate solution but also an accurate…
Fine numerical analysis of the crack-tip position for a Mumford-Shah minimizer
Zhilin Li, Hayk Mikayelyan
A new algorithm to determine the position of the crack (discontinuity set) of certain minimizers of Mumford-Shah functional in situations when a crack-tip occurs is introduced. The…