Abstract
We combine the good properties of recovery-based error estimators with the richness of information typical of an anisotropic a posteriori analysis. This merging yields error estimators which are general purpose yet simple and easy to implement, and automatically incorporate detailed geometric information about the computational mesh. This allows us to devise an effective anisotropic mesh adaptation procedure suited to control the discretization error both in the energy norm and in a goal-oriented framework. The advection-diffusion-reaction problem is considered as a computational paradigm.
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Notes
- 1.
Indeed, picking \(J_{2}(\varphi ) = a(\varphi ,u)\), we get that \(J_{2}(e_{h}) = a(e_{h},u) = a(e_{h},e_{h})\), thanks to the Galerkin orthogonality.
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Micheletti, S., Perotto, S. (2013). Anisotropic Recovery-Based a Posteriori Error Estimators for Advection-Diffusion-Reaction Problems. In: Cangiani, A., Davidchack, R., Georgoulis, E., Gorban, A., Levesley, J., Tretyakov, M. (eds) Numerical Mathematics and Advanced Applications 2011. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-33134-3_5
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DOI: https://doi.org/10.1007/978-3-642-33134-3_5
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