Increased attention has been paid on numerical modeling of interface problems as its wide
applications in various aspects of science. Motivated by enhancing the application of the …

In the present paper, we develop a local meshless procedure for solving a steady state two-
dimensional interface problem having discontinuous coefficients and curved interfaces with …

A new augmented method is proposed for elliptic interface problems with a piecewise
variable coefficient that has a finite jump across a smooth interface. The main motivation is to …

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

A high-order cut finite element method is formulated for solving the elastic wave equation.
Both a single domain problem and an interface problem are treated. The boundary or …

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 …

In this paper, an efficient numerical method is proposed for the 1D elliptic type interface
problems. We first construct a broken reproducing kernel space and then apply the …

Many practical problems, including modeling composite materials, nuclear waste disposal,
oil reservoir simulations, and flows in porous medium, commonly involve interface problems …

In this work, we propose efficient and accurate numerical algorithms based on difference
potentials method for numerical solution of chemotaxis systems and related models in 3D …

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 …