Abstract
We consider a family of two-weight finite difference schemes for a time-dependent advection-diffusion problem. For a given uniform grid-spacing in time and space, and for a fixed value of advection and diffusion parameters, we demonstrate how to optimally choose these weights by means of the notion of an equivalent differential equation. We also provide a geometric interpretation of the weights. We present numerical results that demonstrate that the approach is superior to other commonly used methods that also fit into the framework of a two-weight scheme.
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Acknowledgements
This material is based upon works supported by the Science Foundation Ireland under Grant No. 08/RFP/CMS1205.
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Chadha, N.M., Madden, N. (2011). A Two-Weight Scheme for a Time-Dependent Advection-Diffusion Problem. In: Clavero, C., Gracia, J., Lisbona, F. (eds) BAIL 2010 - Boundary and Interior Layers, Computational and Asymptotic Methods. Lecture Notes in Computational Science and Engineering, vol 81. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-19665-2_11
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DOI: https://doi.org/10.1007/978-3-642-19665-2_11
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