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The immersed finite volume element methods for the elliptic interface problems

Author

Listed:
  • Ewing, Richard E.
  • Li, Zhilin
  • Lin, Tao
  • Lin, Yanping

Abstract

An immersed finite element space is used to solve the elliptic interface problems by a finite volume element method. Special nodal basis functions are introduced in a triangle whose interior intersects with the interface so that the jump conditions across the interface are satisfied. Optimal error estimates in an energy norm are obtained. Numerical results are supplied to justify the theoretical work and to reveal some interesting features of the method.

Suggested Citation

  • Ewing, Richard E. & Li, Zhilin & Lin, Tao & Lin, Yanping, 1999. "The immersed finite volume element methods for the elliptic interface problems," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 50(1), pages 63-76.
    • Handle: RePEc:eee:matcom:v:50:y:1999:i:1:p:63-76
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    Cited by:

    1. Ahmed Ullah, Sheik & Zhao, Shan, 2020. "Pseudo-transient ghost fluid methods for the Poisson-Boltzmann equation with a two-component regularization," Applied Mathematics and Computation, Elsevier, vol. 380(C).
    2. Coco, A. & Semplice, M. & Serra Capizzano, S., 2020. "A level-set multigrid technique for nonlinear diffusion in the numerical simulation of marble degradation under chemical pollutants," Applied Mathematics and Computation, Elsevier, vol. 386(C).
    3. Peng, Jie & Shu, Shi & Yu, HaiYuan & Feng, Chunsheng & Kan, Mingxian & Wang, Ganghua, 2017. "Error estimates on a finite volume method for diffusion problems with interface on rectangular grids," Applied Mathematics and Computation, Elsevier, vol. 311(C), pages 335-352.
    4. Mengya Su & Liuqing Xie & Zhiyue Zhang, 2022. "Numerical Analysis of Fourier Finite Volume Element Method for Dirichlet Boundary Optimal Control Problems Governed by Elliptic PDEs on Complex Connected Domains," Mathematics, MDPI, vol. 10(24), pages 1-26, December.
    5. Feng, Qiwei & Han, Bin & Minev, Peter, 2022. "A high order compact finite difference scheme for elliptic interface problems with discontinuous and high-contrast coefficients," Applied Mathematics and Computation, Elsevier, vol. 431(C).

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