A modified immersed finite volume element method for elliptic interface problems


  • Quanxiang Wang Nanjing Agricultural University
  • Zhiyue Zhang Nanjing Normal University




modified, control volume, interface problems, Cartesian mesh


This paper presents a new immersed finite volume element method for solving second-order elliptic problems with discontinuous diffusion coefficient on a Cartesian mesh. The new method possesses the local conservation property of classic finite volume element method, and it can overcome the oscillating behaviour of the classic immersed finite volume element method. The idea of this method is to reconstruct the control volume according to the interface, which makes it easy to implement. Optimal error estimates can be derived with respect to an energy norm under piecewise \(H^{2}\) regularity. Numerical results show that the new method significantly outperforms the classic immersed finite volume element method, and has second-order convergence in \(L^{\infty}\) norm.

doi: 10.1017/S1446181120000073

Author Biographies

Quanxiang Wang, Nanjing Agricultural University

College of Engineering, Nanjing Agricultural University, Nanjing 210031, China.

Zhiyue Zhang, Nanjing Normal University

Jiangsu Key Laboratory for NSLSCS, School of Mathematical Sciences, Nanjing Normal University,

Nanjing 210023, China.





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