Interface problems have long been a major focus of scientific computing, leading to the
development of various numerical methods. Traditional mesh-based methods often employ …

This article presents the first higher degree immersed finite element (IFE) method with
proven optimal convergence for elliptic interface problems with nonhomogeneous jump …

This paper presents a new parameter free partially penalized immersed finite element
method and convergence analysis for solving second order elliptic interface problems. A …

This paper designs and analyzes a new and stable Petrov–Galerkin (PG) immersed finite
element method (IFEM) for the second-order elliptic interface problems by introducing …

A discontinuous viscosity coefficient makes the jump conditions of the velocity and normal
stress coupled together, which brings great challenges to some commonly used numerical …

Finite element methods developed for unfitted meshes have been widely applied to various
interface problems. However, many of them resort to non-conforming spaces for …

As a specific type of shape gradient descent algorithm, shape gradient flow is widely used
for shape optimization problems constrained by partial differential equations. In this …

Immersed finite element methods are designed to solve interface problems on interface-
unfitted meshes. However, most of the study, especially analysis, is mainly limited to the two …

A fourth-order unfitted characteristic finite element method (UCFEM) is proposed to solve
free-boundary problems of time-dependent partial differential equations (PDEs). The …

We propose a fourth-order unfitted characteristic finite element method to solve the
advection-diffusion equation on time-varying domains. Based on a characteristic-Galerkin …