Title

A Bilinear Immersed Finite Volume Element Method For the Diffusion Equation with Discontinuous Coefficient

Abstract

This paper is to present a finite volume element (FVE) method based on thebilinear immersed finite element (IFE) for solving the boundary value problems of thediffusion equation with a discontinuous coefficient (interface problem). This methodpossesses the usual FVE method's local conservation property and can use a structuredmesh or even the Cartesian mesh to solve a boundary value problem whose coefficienthas discontinuity along piecewise smooth nontrivial curves. Numerical examples areprovided to demonstrate features of this method. In particular, this method can pro-duce a numerical solution to an interface problem with the usualO(h2) (in L2 norm) an dO(h) (in H1 norm) convergence rates.

Department(s)

Mathematics and Statistics

Keywords and Phrases

Interface Problems; Immersed Interface; Finite Volume Element; Discontinuous Coefficient; Diffusion Equation

Document Type

Article - Journal

Document Version

Citation

File Type

text

Language(s)

English

Rights

© 2009 Global Science Press, All rights reserved.

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