Jimack, P.K. (1996) Optimal eigenvalue and asymtotic large-time approximations using the moving finite-element method. IMA Journal of Numerical Analysis, 16 (3). pp. 381-398. ISSN 0272-4979
The moving finite-element method for the solution of time-dependent partial differential equations is a numerical solution scheme which allows the automatic adaptation of the finite-element approximation space with time, through the use of mesh relocation (r-refinement).
This paper analyzes the asymptotic behaviour of the method for large times when it is applied to the solution of a class of self-adjoint parabolic equations in an arbitrary number of space dimensions. It is shown that asymptotically the method will produce solutions which converge to a fixed mesh and it is proved that such a mesh allows an optimal approximation of the slowest-decaying eigenvalue and eigenfunction for the problem. Hence it is demonstrated that the moving finite-element method can yield an optimal solution to such parabolic problems for large times.
|Copyright, Publisher and Additional Information:||© 1996 by Institute of Mathematics and its Applications. This is an author produced version of a paper published in 'IMA Journal of Numerical Analysis'|
|Keywords:||moving finite elements, eigenvalue problems, best free knot approximations|
|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:||31 Oct 2006|
|Last Modified:||18 Sep 2016 11:20|
|Publisher:||Oxford University Press|