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arXiv · 1402.6402

Model reduction and mesh refinement

Panagiotis Stinis
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Abstract

In recent work we have presented a novel algorithm for mesh refinement which utilizes a reduced model. In particular, the reduced model is used to monitor the transfer of activity (e.g. mass, energy) from larger to smaller scales. When the activity transfer rate exceeds a prescribed tolerance, the algorithm refines the mesh accordingly. The algorithm was applied to the inviscid Burgers and focusing Schr\"odinger equations to detect singularities. We offer here a simple proof of why the use of a reduced model for mesh refinement is a good idea. We do so by showing that by controlling the transfer of activity rate one controls the error caused inevitably by a finite resolution.

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Panagiotis Stinis. 2014-02-26. Model reduction and mesh refinement. https://arxiv.org/abs/1402.6402

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