In this paper, we develop sixth-order hybrid finite difference methods (FDMs) for the elliptic
interface problem−∇⋅(a∇ u)= f in Ω﹨ Γ, where Γ is a smooth interface inside Ω. The …

In this paper we develop finite difference schemes for elliptic problems with piecewise
continuous coefficients that have (possibly huge) jumps across fixed internal interfaces. In …

In this paper, we discuss the second-order finite element method (FEM) and finite difference
method (FDM) for numerically solving elliptic cross-interface problems characterized by …

We propose an approach based on Fourier analysis to wavenumber explicit sharp
estimation of absolute and relative errors of finite difference methods for the Helmholtz …

This paper introduces a wavelet Galerkin method for solving two-dimensional elliptic
interface problems of the form in $-\nabla\cdot (a\nabla u)= f $ in $\Omega\backslash …

Most numerical approximations of frequency-domain wave propagation problems suffer from
the so-called dispersion error, which is the fact that plane waves at the discrete level …

In this paper, we develop sixth-order hybrid finite difference methods (FDMs) for the elliptic
interface problem $-\nabla\cdot (a\nabla u)= f $ in $\Omega\backslash\Gamma $, where …

For elliptic interface problems with discontinuous coefficients, the maximum accuracy order
for compact 9-point finite difference scheme in irregular points is three [7]. The discontinuous …

Ce manuscrit est une synthèse de mes activités de recherche réalisées depuis mon
recrutement en tant que Maître de conférences. Une première partie décrit mon curriculum …

Acoustic fields with impedance boundary conditions have high engineering applications,
such as noise control and evaluation of sound insulation materials, and can be …