Adaptive Grid Methods - An Introduction

Craig Chapman

Friday 13th November, 2009 16:00-17:00 Mathematics Building, room 325


In many fields of science and engineering it is necessary to compute numerical solutions to ODEs and PDEs in order to gain an understanding of any possible solutions, however, in many situations, such as shock formation, changes of phase and in regions of complexity, a fixed grid method is unable to fully capture the solution profile. Adaptive grid methods aim to overcome this difficulty by adapting the position of the underlying numerical grid to better suit the evolving profile. Several methods for this have been proposed, I hope to briefly introduce these methods and in particular talk about the so called 'r-adaptivite' method. Theory will, hopefully, be supplemented by some illustrative examples and movies where available. Some understanding of basic numerical methods (e.g. finite differences) would be useful but shouldn't be necessary.

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