This article develops and analyzes ap th degree immersed finite element (IFE) method for
solving the elliptic interface problems with meshes independent of the coefficient …

In this paper, the difference potentials method-based ADI finite difference scheme is
proposed for numerical solutions of two-dimensional nonlinear convection–diffusion …

We solve the wave equation with variable wave speed on nonconforming domains with
fourth order accuracy in both space and time. This is accomplished using an implicit finite …

A new numerical approach for the time independent Helmholtz equation on irregular
domains has been developed. Trivial Cartesian meshes and simple 9-point stencil …

We present a robust and effective method for the numerical solution of the biharmonic
interface problem with discontinuities in both the solution and its derivatives. We use a …

Here, we extend the optimal local truncation error method (OLTEM) recently developed in
our papers to the 3D time-independent Helmholtz equation on irregular domains. Trivial …

Standard numerical methods often fail to solve the Helmholtz equation accurately near
reentrant corners, since the solution may become singular. The singularity has an …

Many wave propagation problems involve discontinuous material properties. We propose to
solve such problems by non-overlapping domain decomposition combined with the method …

In this work, we discuss and compare three methods for the numerical approximation of
constant-and variable-coefficient diffusion equations in both single and composite domains …

In this paper, we present a robust and accurate numerical algorithm for solving the nonlinear
Poisson–Boltzmann equation, based on the difference potentials method (DPM). First, we …