Jimack, P.K. (1996) A best approximation property of the moving finite element method. SIAM Journal of Numerical Analysis, 33 (6). pp. 2286-2302. ISSN 00361429Full text available as:
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The moving finite element method (MFE) for the solution of time-dependent partial differential equations (PDEs) is a numerical solution scheme which allows the automatic adaption of the finite element approximation space with time. An analysis of how this method models the steady solutions of a general class of parabolic linear source equations is presented.
It is shown that under certain conditions the steady solutions of the MFE problem can correspond to best free knot spline approximations to the true steady solution of the differential equation when using the natural norm associated with the problem. Hence a quantitative measure of the advantages of the MFE method over the usual fixed grid Galerkin method is produced for these equations. A number of numerical examples are included to illustrate these results.
|Copyright, Publisher and Additional Information:||© 1996 Society for Industrial and Applied Mathematics. This is an author produced version of a paper published in 'SIAM Journal of Numerical Analysis'|
|Keywords:||moving finite element; steady solutions; best free knot approximations|
|Academic Units:||The University of Leeds > Faculty of Engineering (Leeds) > School of Computing (Leeds)|
|Depositing User:||Repository Assistant|
|Date Deposited:||26 Oct 2006|
|Last Modified:||08 Feb 2013 17:02|
|Publisher:||Society for Industrial and Applied Mathematics|
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