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Title: Modelling time-dependent partial differential equations using a moving mesh approach based on conservation
Author: Lee, Tamsin E.
ISNI:       0000 0004 2716 7257
Awarding Body: University of Reading
Current Institution: University of Reading
Date of Award: 2011
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One of the advantages of moving mesh methods for the numerical solution of partial dif- ferential equations is their ability to track moving boundaries. In this thesis we propose a velocity-based moving mesh method in which we primarily focus on moving the nodes so as to preserve local mass fractions. To recover the solutions from the mesh we use an integral approach which avoids altering the structure of the original equations when incor- porating the velocity. We apply our method to a range of moving boundary problems: the porous medium equation; Richards' equation; the Crank-Gupta problem; an avascular tu- mour growth model. We compare the numerical results to exact solutions where possible, or to results obtained from other methods, and find that our approach is accurate. We apply three different strategies to the tumour growth model, using information from the previous chapters, which enables us to make comparisons between the different approaches. We conclude that our moving mesh method can offer equal accuracy and better resolution, whilst offering greater flexibility than a standard fixed mesh approach.
Supervisor: Not available Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available