Journal
COMMUNICATIONS IN COMPUTATIONAL PHYSICS
Volume 6, Issue 1, Pages 185-202Publisher
GLOBAL SCIENCE PRESS
DOI: 10.4208/cicp.2009.v6.p185
Keywords
Interface problems; immersed interface; finite volume element; discontinuous coefficient; diffusion equation
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Funding
- NSF [DMS-0713763]
- NSERC (Canada).
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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 WE 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(h(2)) (in L-2 norm) and O(h) (in H-1 norm) convergence rates.
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