C. Erath, S. Funken, D. Praetorius:

"Adaptive cell-centered finite volume method";

in: "ASC Report 01/2008", issued by: Institute for Analysis and Scientific Computing; Vienna University of Technology, Wien, 2008, ISBN: 978-3-902627-01-8.

We propose an adaptive mesh-refining strategy for the cell-centered

FVM based on some a~posteriori error control for the quantity

$\norm{\nabla_\TT(u-\II u_h)}{L^2}$. Here, $u_h\in \PP^0(\TT)$

denotes the FVM approximation of $u$ and $\I$ is a certain

interpolation operator. As model example serves the Laplace equation

with mixed boundary conditions, where our contributions extend a

result of [Nicaise, SINUM 2005]. Moreover, this approach allows the

coupling of finite volume schemes with the boundary element method,

which is a new and fruitful combination of the FVM with ideas from

[Carstensen, Funken, COMPUTING 1999].

http://www.asc.tuwien.ac.at/preprint/2008/asc01x2008.pdf

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