Interface problems arise in many applications. For example, when there are two different
materials, such as water and oil, or the same material but at different states, such as water …

We present a general error estimation framework for a finite volume element (FVE) method
based on linear polynomials for solving second-order elliptic boundary value problems. This …

A new weak Galerkin (WG) finite element method is introduced and analyzed in this paper
for solving second order elliptic equations with discontinuous coefficients and interfaces …

This article discusses an immersed finite element (IFE) space introduced for solving a
second‐order elliptic boundary value problem with discontinuous coefficients (interface …

This paper is to develop immersed finite element (IFE) functions for solving second order
elliptic boundary value problems with discontinuous coefficients and non-homogeneous …

Weak Galerkin methods refer to general finite element methods for partial differential
equations (PDEs) in which differential operators are approximated by their weak forms as …

This article discusses a bilinear immersed finite element (IFE) space for solving second‐
order elliptic boundary value problems with discontinuous coefficients (interface problem) …

This paper presents two immersed finite element (IFE) methods for solving the elliptic
interface problem arising from electric field simulation in composite materials. The meshes …

We introduce a simple method, dubbed the Voronoi Interface Method, to solve Elliptic
problems with discontinuities across the interface of irregular domains. This method …

This paper proves the convergence of the ghost fluid method for second order elliptic partial
differential equations with interfacial jumps. A weak formulation of the problem is first …