Baines, M.J., Hubbard, M.E., Jimack, P.K. and Jones, A.C. (2006) Scale-invariant moving finite elements for nonlinear partial differential equations in two dimensions. Applied Numerical Mathematics, 56 (2). pp. 230-252. ISSN 0168-9274
A scale-invariant moving finite element method is proposed for the adaptive solution of nonlinear partial differential equations. The mesh movement is based on a finite element discretisation of a scale-invariant conservation principle incorporating a monitor function, while the time discretisation of the resulting system of ordinary differential equations is carried out using a scale-invariant time-stepping which yields uniform local accuracy in time.
The accuracy and reliability of the algorithm are successfully tested against exact self-similar solutions where available, and otherwise against a state-of-the-art h-refinement scheme for solutions of a two-dimensional porous medium equation problem with a moving boundary. The monitor functions used are the dependent variable and a monitor related to the surface area of the solution manifold.
|Copyright, Publisher and Additional Information:||© 2005 IMACS. This is an author produced version of a paper published in 'Applied Numerical Mathematics'.|
|Keywords:||Scale invariance, Moving meshes, Finite element method, Porous medium equation, Moving boundaries|
|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:||13 Dec 2006|
|Last Modified:||17 Sep 2016 17:54|