C. Erath, D. Praetorius:

"A Posteriori Error Estimate and Adaptive Mesh-Refinement for the Cell-Centered Finite Volume Method for Elliptic Boundary Value Problems";

in: "ASC Report 02/2007", issued by: Institute for Analysis and Scientific Computing; Vienna University of Technology, Wien, 2007, ISBN: 978-3-902627-00-1.

We extend a result of Nicaise (SINUM 2005) for the aposteriori

error estimation of the cell-centered finite volume method for the

numerical solution of elliptic problems. Having computed the

piecewise constant finite volume solution $u_h$, we compute a

Morley-type interpolant $\II u_h$. For the exact solution $u$, the

energy error $\norm{\nabla_\TT(u-\II u_h)}{L^2}$ can be controlled

efficiently and reliably by a residual-based a~posteriori error

estimator $\eta$. The local contributions of $\eta$ are used to

steer an adaptive mesh-refining algorithm. As model example serves

the Laplace equation in 2D with mixed Dirichlet-Neumann boundary

conditions.

http://www.asc.tuwien.ac.at/preprint/2007/asc02x2007.pdf

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