A bilinear immersed finite volume element method for the diffusion equation with discontinuous coefficient

X. M. He, T. Lin, Yanping Lin

Research output: Journal article publicationJournal articleAcademic researchpeer-review

44 Citations (Scopus)

Abstract

This paper is to present a finite volume element (FVE) method based on the bilinear immersed finite element (IFE) for solving the boundary value problems of the diffusion equation with a discontinuous coefficient (interface problem). This method possesses the usual FVE method's local conservation property and can use a structured mesh or even the Cartesian mesh to solve a boundary value problem whose coefficient has discontinuity along piecewise smooth nontrivial curves. Numerical examples are provided to demonstrate features of this method. In particular, this method can produce a numerical solution to an interface problem with the usual O(h2) (in L2norm) and O(h) (in H1norm) convergence rates.
Original languageEnglish
Pages (from-to)185-202
Number of pages18
JournalCommunications in Computational Physics
Volume6
Issue number1
DOIs
Publication statusPublished - 1 Jan 2009

Keywords

  • Diffusion equation
  • Discontinuous coefficient
  • Finite volume element
  • Immersed interface
  • Interface problems

ASJC Scopus subject areas

  • Physics and Astronomy (miscellaneous)

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