A Bilinear Immersed Finite Volume Element Method for the Diffusion Equation with Discontinuous Coefficient
Year: 2009
Communications in Computational Physics, Vol. 6 (2009), Iss. 1 : pp. 185–202
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 L2 norm) and O(h) (in H1 norm) convergence rates.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2009-CiCP-7677
Communications in Computational Physics, Vol. 6 (2009), Iss. 1 : pp. 185–202
Published online: 2009-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 18
Keywords: Interface problems immersed interface finite volume element discontinuous coefficient diffusion equation.