C. Erath, D. Praetorius:
"A Posteriori Error Estimate and Adaptive Mesh-Refinement for the Cell-Centered Finite Volume Method for Elliptic Boundary Value Problems";
SIAM Journal on Numerical Analysis, 47 (2008), 1; S. 109 - 135.

Kurzfassung englisch:
We extend a result of Nicaise [SIAM J. Numer. Anal., 43 (2005), pp.
1481-1503] for the a posteriori 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 $\mathcal{I} u_h$. For the exact
solution $u$, the energy error $\norm{\nabla_{\mathcal{T}}
(u-\mathcal{I} u_h)}{L^2}$ 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. A model example serves the Laplace equation in two
dimensions with mixed Dirichlet-Neumann boundary conditions.

Finite Volume Method, Cell-Centred FVM, Adaptive Algorithm

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