Finite element methods for electromagnetic problems modeled by Maxwell-type equations
are highly sensitive to the conformity of approximation spaces, and non-conforming methods …

Immersed finite element (IFE) methods are a group of long-existing numerical methods for
solving interface problems on unfitted meshes. A core argument of the methods is to avoid a …

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

In this article, we develop a Taylor-Hood immersed finite element (IFE) method to solve two-
dimensional Stokes interface problems. The P2-P1 local IFE spaces are constructed using …

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 …

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 …

In the paper we develop the optimal local truncation error method (OLTEM) with the non-
diagonal and diagonal mass matrices on unfitted Cartesian meshes for the 3-D time …

A new conforming discontinuous Galerkin method, which is based on weak Galerkin finite
element method, is introduced for solving second order elliptic interface problems with …

This paper presents the first numerical attempt on fourth-order interface problems on
surfaces. A mixed immersed surface finite element method based on Ciarlet-Raviart …

In this paper, a selective discontinuous Galerkin (SDG) method and a polynomial preserving
recovery (PPR) method are developed and integrated with the immersed-finite-element …