An Optimal Multigrid Algorithm for the Combining P1-Q1 Finite Element Approximations of Interface Problems Based on Local Anisotropic Fitting Meshes

A new finite element method is proposed for second order elliptic interface problems based on a local anisotropic fitting mixed mesh. The local anisotropic fitting mixed mesh is generated from an interface-unfitted mesh by simply connecting the intersected points of the interface and the underlying...

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Bibliographic Details
Published in:Journal of scientific computing Vol. 88; no. 1; p. 16
Main Authors: Hu, Jun, Wang, Hua
Format: Journal Article
Language:English
Published: New York Springer US 01.07.2021
Springer Nature B.V
Subjects:
Algorithms
Approximation
Computational Mathematics and Numerical Analysis
Convergence
Discrete systems
Finite element method
Interfaces
Mathematical analysis
Mathematical and Computational Engineering
Mathematical and Computational Physics
Mathematics
Mathematics and Statistics
Mesh generation
Methods
Partial differential equations
Theoretical
Interface-fitted mesh
Multigrid method
Anisotropic element
ISSN:0885-7474, 1573-7691
Online Access:Get full text
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Summary:A new finite element method is proposed for second order elliptic interface problems based on a local anisotropic fitting mixed mesh. The local anisotropic fitting mixed mesh is generated from an interface-unfitted mesh by simply connecting the intersected points of the interface and the underlying mesh successively. Optimal approximation capabilities on anisotropic elements are proved, the convergence rates are linear and quadratic in H 1 and L 2 norms, respectively. The discrete system is usually ill-conditioned due to anisotropic and small elements near the interface. Thereupon, a new multigrid method is presented to handle this issue. The convergence rate of the multigrid method is shown to be optimal with respect to both the coefficient jump ratio and mesh size. Numerical experiments are presented to demonstrate the theoretical results.
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ISSN:0885-7474
1573-7691
DOI:10.1007/s10915-021-01536-6