Corpus ID: 236772028

Immersed Virtual Element Methods for Elliptic Interface Problems

@article{Cao2021ImmersedVE,
  title={Immersed Virtual Element Methods for Elliptic Interface Problems},
  author={Shuhao Cao and Long Chen and Ruchi Guo and Frank Lin},
  journal={ArXiv},
  year={2021},
  volume={abs/2108.00619}
}
  • Shuhao Cao, Long Chen, +1 author Frank Lin
  • Published 2021
  • Computer Science, Mathematics
  • ArXiv
This article presents an immersed virtual element method for solving a class of interface problems that combines the advantages of both body-fitted mesh methods and unfitted mesh methods. A background body-fitted mesh is generated initially. On those interface elements, virtual element spaces are constructed as solution spaces to local interface problems, and exact sequences can be established for these new spaces involving discontinuous coefficients. The discontinuous coefficients of interface… Expand

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References

SHOWING 1-10 OF 60 REFERENCES
The adaptive immersed interface finite element method for elliptic and Maxwell interface problems
TLDR
Self-adaptive finite element methods with error control for solving elliptic and electromagnetic problems with discontinuous coefficients and flexible h- Adaptive strategies are developed, which can be systematically extended to a large class of interface problems. Expand
Partially Penalized Immersed Finite Element Methods For Elliptic Interface Problems
TLDR
New immersed finite element (IFE) methods for solving the popular second order elliptic interface problems on structured Cartesian meshes even if the involved interfaces have nontrivial geometries are presented. Expand
The immersed interface method using a finite element formulation
A finite element method is proposed for one dimensional interface problems involving discontinuities in the coefficients of the differential equations and the derivatives of the solutions. TheExpand
An interface-fitted mesh generator and virtual element methods for elliptic interface problems
Abstract A simple and efficient interface-fitted mesh generation algorithm which can produce a semi-structured interface-fitted mesh in two and three dimensions quickly is developed in this paper.Expand
An immersed Raviart-Thomas mixed finite element method for elliptic interface problems on unfitted meshes
This paper presents a lowest-order immersed Raviart-Thomas mixed triangular finite element method for solving elliptic interface problems on unfitted meshes independent of the interface. In order toExpand
An interface-fitted adaptive mesh method for elliptic problems and its application in free interface problems with surface tension
TLDR
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. Expand
A group of immersed finite-element spaces for elliptic interface problems
We present a unified framework for developing and analysing immersed finite element (IFE) spaces for solving typical elliptic interface problems with interface independent meshes. This frameworkExpand
High-order extended finite element methods for solving interface problems
In this paper, we study arbitrary order extended finite element (XFE) methods based on two discontinuous Galerkin (DG) schemes in order to solve elliptic interface problems in two and threeExpand
An immersed finite element space and its approximation capability
This article discusses an immersed finite element (IFE) space introduced for solving a second-order elliptic boundary value problem with discontinuous coefficients (interface problem). The IFE spaceExpand
Approximation capabilities of immersed finite element spaces for elasticity Interface problems
We construct and analyze a group of immersed finite element (IFE) spaces formed by linear, bilinear and rotated Q1 polynomials for solving planar elasticity equation involving interface. The shapeExpand
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