This article presents new immersed finite element (IFE) methods for solving the popular
second order elliptic interface problems on structured Cartesian meshes even if the involved …

We present a unified framework for developing and analyzing immersed finite-element (IFE)
spaces for solving typical elliptic interface problems with interface-independent meshes …

Motivated by the need to handle complex boundary conditions efficiently and accurately in
particle-in-cell (PIC) simulations, this paper presents a three-dimensional (3D) linear …

This paper is for proving that the partially penalized immersed finite element (PPIFE)
methods developed in [25] converge optimally under the standard piecewise H2 regularity …

The purpose of this article is to propose and analyze a new coupled multiphysics model and
a decoupled stabilized finite element method for the closed-loop geothermal system, which …

In this paper, we introduce a class of lowest-order nonconforming immersed finite element
(IFE) methods for solving two-dimensional Stokes interface problems. The proposed …

We present partially penalized immersed finite element methods for solving parabolic
interface problems on Cartesian meshes. Typical semidiscrete and fully discrete schemes …

A new immersed finite element (IFE) method is developed for second-order elliptic problems
with discontinuous diffusion coefficient. The IFE space is constructed based on the rotated …

In this article, we study superconvergence properties of immersed finite element methods for
the one dimensional elliptic interface problem. Due to low global regularity of the solution …

Anisotropic diffusion is important to many different types of common materials and media.
Based on structured Cartesian meshes, we develop a three‐dimensional (3D) …