On the relationship between the moving finite-element procedure and best piecewiseL2 fits with adjustable nodes

It is shown that, for a class of time-dependent partial differential equations of the form ut = ℒu, one step of the moving finite-element (MFE) procedure corresponds to one iteration of an algorithm for obtaining best L2 fits with adjustable nodes to continuous functions. In the steady-state limit the MFE procedure gives the best fit of ℒu, with adjustable nodes, to the null function. For first-order partial differential equations, the MFE procedure moves nodes with approximate characteristic nodal speeds. We identify an additional speed component arising directly from the L2 projection which seeks a best fit in the sense described above. © 1994 John Wiley & Sons, Inc.