A Best Approximation Property of the Moving Finite Element Method
نویسنده
چکیده
The Moving Finite Element method for the solution of time-dependent partial dierential equations is a numerical solution scheme which allows the automatic adaption of the nite 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 the steady solutions of the Moving Finite Element problem correspond to best free knot spline approximations to the true steady solution of the dierential equation when using a particular norm. Hence a quantitative measure of the advantages of the Moving Finite Element method over the usual xed grid Galerkin method is produced for these equations. A number of numerical examples are included to illustrate these results.
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