132 citations · 497 across the 66 of their papers we have counts for
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A new approach for numerical simulation of the time-dependent Ginzburg-Landau equations
Buyang Li, Zhimin Zhang
We introduce a new approach for finite element simulations of the time-dependent Ginzburg-Landau equations (TDGL) in a general curved polygon, possibly with reentrant corners. Spec…
Mathematical and numerical analysis of time-dependent Ginzburg--Landau equations in nonconvex polygons based on Hodge decomposition
Buyang Li, Zhimin Zhang
We prove well-posedness of time-dependent Ginzburg--Landau system in a nonconvex polygonal domain, and decompose the solution as a regular part plus a singular part. We see that th…
Spectral method for substantial fractional differential equations
Can Huang, Qingshuo Song, Zhimin Zhang
In this paper, a non-polynomial spectral Petrov-Galerkin method and associated collocation method for substantial fractional differential equations (FDEs) are proposed, analyzed, a…
Hessian Recovery for Finite Element Methods
Hailong Guo, Zhimin Zhang, Ren Zhao
In this article, we propose and analyze an effective Hessian recovery strategy for the Lagrangian finite element of arbitrary order . We prove that the proposed Hessian recovery…
Superconvergent Two-grid Methods For Elliptic Eigenvalue Problems
Hailong Guo, Zhimin Zhang, Ren Zhao
Some numerical algorithms for elliptic eigenvalue problems are proposed, analyzed, and numerically tested. The methods combine advantages of the two-grid algorithm, two-space metho…
Superconvergence of Local Discontinuous Galerkin method for one-dimensional linear parabolic equations
Waixiang Cao, Zhimin Zhang
In this paper, we study superconvergence properties of the local discontinuous Galerkin method for one-dimensional linear parabolic equations when alternating fluxes are used. We p…