An interface-fitted mesh generator and virtual element methods for elliptic interface problems

  title={An interface-fitted mesh generator and virtual element methods for elliptic interface problems},
  author={Long Chen and Huayi Wei and Min Wen},
  journal={J. Comput. Phys.},

Finite Element Methods For Interface Problems On Local Anisotropic Fitting Mixed Meshes

A simple and efficient interface-fitted mesh generation algorithm which can produce a local anisotropic fitting mixed mesh which consists of both triangles and quadrilaterals near the interface and a new finite element method is proposed for second order elliptic interface problems based on the resulting mesh.

Solving Three-Dimensional Interface Problems with Immersed Finite Elements: A-Priori Error Analysis

A Virtual Finite Element Method for Two Dimensional Maxwell Interface Problems with a Background Unfitted Mesh

A novel virtual space is introduced on a virtual triangulation of the polygonal mesh satisfying a maximum angle condition, which shares exactly the same degrees of freedom as the usual $\bfH(\curl)$-conforming virtual space.

A Trilinear Immersed Finite Element Method for Solving Elliptic Interface Problems

This article presents an immersed finite element (IFE) method for solving the typical three-dimensional second order elliptic interface problem with an interface-independent Cartesian mesh. The local

Adaptive Surface Fitting and Tangential Relaxation for High-Order Mesh Optimization

A new approach for controlling the characteristics of certain mesh faces during optimization of high-order curved meshes is proposed, which completely avoids geometric operations (e.g., surface projections), and all calculations can be performed through discrete element operations.

A priori error analysis of virtual element method for contact problem

  • Fei WangB. Reddy
  • Computer Science
    Fixed Point Theory and Algorithms for Sciences and Engineering
  • 2022
It is proved that the lowest-order VEM achieves linear convergence order, which is optimal, and established a priori error estimate of the virtual element method for the contact problem.

Auxiliary space preconditioners for virtual element methods on polytopal meshes.

The auxiliary space preconditioners for solving the linear system arising from the virtual element methods discretization on polytopal meshes for the second order elliptic equations are developed.



New Cartesian grid methods for interface problems using the finite element formulation

New finite element methods based on Cartesian triangulations are presented for two dimensional elliptic interface problems involving discontinuities in the coefficients, and these new methods can be used as finite difference methods.


A finite element method for elasticity systems with discontinuities in the coefficients and the flux across an arbitrary interface is proposed in this paper and local modifications lead to a quasi-uniform body-fitted mesh from the original Cartesian mesh.

A finite element method for interface problems in domains with smooth boundaries and interfaces

It is shown that the error in the finite element approximation is of optimal order for linear elements on a quasiuniform triangulation.

An interface-fitted adaptive mesh method for elliptic problems and its application in free interface problems with surface tension

A simple piecewise linear finite element method is developed built on this interface-fitted adaptive mesh method and it is proved its almost optimal convergence for elliptic problems with jump conditions across the interface.

A new multiscale finite element method for high-contrast elliptic interface problems

We introduce a new multiscale finite element method which is able to accurately capture solutions of elliptic interface problems with high contrast coefficients by using only coarse quasiuniform

Immersed finite element methods for elliptic interface problems with non-homogeneous jump conditions

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

The Immersed Interface/Multigrid Methods for Interface Problems

The second order maximum principle preserving finite difference scheme for linear parabolic equations, using the Crank--Nicolson scheme to deal with the diffusion part and an explicit scheme for the first order derivatives is developed.

Three‐dimensional immersed finite element methods for electric field simulation in composite materials

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 used in these IFE

A geometric toolbox for tetrahedral finite element partitions

A survey of some geometric results on tetrahedral partitions and their refinements in a unified manner and special emphasis is laid on the correspondence between relevant results and terminology used in FE computations, and those established in the area of discrete and computational geometry (DCG).