Baines, M.J., Hubbard, M.E. and Jimack, P.K. (2005) A moving mesh finite element algorithm for the adaptive solution of time-dependent partial differential equations with moving boundaries. Applied Numerical Mathematics, 54 (3-4). pp. 450-469. ISSN 0168-9274
Available under licence : See the attached licence file.
A moving mesh finite element algorithm is proposed for the adaptive solution of nonlinear diffusion equations with moving boundaries in one and two dimensions. The moving mesh equations are based upon conserving a local proportion, within each patch of finite elements, of the total “mass” that is present in the projected initial data. The accuracy of the algorithm is carefully assessed through quantitative comparison with known similarity solutions, and its robustness is tested on more general problems.
Applications are shown to a variety of problems involving time-dependent partial differential equations with moving boundaries. Problems which conserve mass, such as the porous medium equation and a fourth order nonlinear diffusion problem, can be treated by a simplified form of the method, while problems which do not conserve mass require the full theory.
|Copyright, Publisher and Additional Information:||© 2004 IMACS. This is an author produced version of a paper published in 'Applied Numerical Mathematics'.|
|Institution:||The University of Leeds|
|Academic Units:||The University of Leeds > Faculty of Engineering (Leeds) > School of Computing (Leeds)|
|Depositing User:||Repository Assistant|
|Date Deposited:||14 Dec 2006|
|Last Modified:||10 Jun 2014 18:27|