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

@article{Chen2017AnIM, 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.}, year={2017}, volume={334}, pages={327-348} }

## 76 Citations

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

- Computer ScienceArXiv
- 2020

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

- Computer ScienceJ. Comput. Phys.
- 2021

### An immersed finite element method for elliptic interface problems in three dimensions

- MathematicsJ. Comput. Phys.
- 2020

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

- Computer ScienceMathematical Models and Methods in Applied Sciences
- 2021

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

- Mathematics
- 2019

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

- Computer ScienceArXiv
- 2021

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

- Computer ScienceFixed 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.

### A two-grid method for semi-linear elliptic interface problems by partially penalized immersed finite element methods

- Computer Science, MathematicsMath. Comput. Simul.
- 2020

### Auxiliary space preconditioners for virtual element methods on polytopal meshes.

- Computer Science
- 2018

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.

### A least-squares virtual element method for second-order elliptic problems

- Computer ScienceComput. Math. Appl.
- 2020

## References

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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.

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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.

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