Publications in Scientific Journals:
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;
109
- 135.
English abstract:
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.
Keywords:
Finite Volume Method, Cell-Centred FVM, Adaptive Algorithm
"Official" electronic version of the publication (accessed through its Digital Object Identifier - DOI)
http://dx.doi.org/10.1137/070702126
Electronic version of the publication:
http://dx.doi.org/10.1137/070702126
Created from the Publication Database of the Vienna University of Technology.