The recent development of machine learning (ML) and Deep Learning (DL) increases the
opportunities in all the sectors. ML is a significant tool that can be applied across many …

We develop a finite element adaptive strategy with error control for the wave scattering by
periodic structures. The unbounded computational domain is truncated to a bounded one by …

We develop an adaptive perfectly matched layer (PML) technique for solving the time-
harmonic scattering problems. The PML parameters such as the thickness of the layer and …

An efficient and reliable a posteriori error estimate is derived for linear parabolic equations
which does not depend on any regularity assumption on the underlying elliptic operator. An …

The successful implementation of adaptive finite element methods based on a posteriori
error estimates depends on several ingredients: an a posteriori error indicator, a …

In this paper, we review various methods for the numerical approximations of the Ginzburg–
Landau models of superconductivity. Particular attention is given to the different treatment of …

In this paper we prove the uniform convergence of the standard multigrid V-cycle algorithm
with the Gauss-Seidel relaxation performed only on the new nodes and their “immediate” …

In this paper, we study linearized Crank--Nicolson Galerkin finite element methods for time-
dependent Ginzburg--Landau equations under the Lorentz gauge. We present an optimal …

We study the rate of convergence of some finite difference schemes to solve the two‐
dimensional Ginzburg‐Landau equation. Avoiding the difficulty in estimating the numerical …

We develop an adaptive edge finite element method based on reliable and efficient residual-
based a posteriori error estimates for low-frequency time-harmonic Maxwell equations with …