The behavior of vortex matter in high-temperature superconductors (HTS) controls the entire
electromagnetic response of the material, including its current carrying capacity. Here, we …

In this paper, an effective linearized element-free Galerkin (EFG) method is developed for
the numerical solution of the complex Ginzburg–Landau (GL) equation. To deal with the time …

We use time-dependent Ginzburg-Landau theory to study the nucleation of vortices in type-II
superconductors in the presence of both geometric and material inhomogeneities. The …

This paper focuses on a new error analysis and a recovering technique of frequently-used
mixed FEMs for a dynamical incompressible magnetohydrodynamics (MHD) system. The …

In this paper, the error analysis of a two-grid method (TGM) with backward Euler scheme is
discussed for semilinear parabolic equation. Contrary to the conventional finite element …

In this paper we propose an efficient numerical scheme for solving the phase field model
(PFM) of corrosive dissolution that is linear and second-order accurate in both time and …

We propose and analyze residual-based a posteriori error estimator for a new finite element
method for the time-dependent Ginzburg–Landau equations with the temporal gauge of …

This paper is concerned with numerical analysis of a finite element method for the time-
dependent Ginzburg–Landau equations under the Coulomb gauge. The main challenge is …

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 …

In this paper, the second-order weighted implicit-explicit (IMEX) finite element method (FEM)
is presented for the nonlinear Ginzburg-Landau equation (GLE). We mainly focus on a …