Abstract
Moving-grid methods in one space dimension have become popular for solving several kinds of parabolic and hyperbolic partial differential equations (PDEs) involving fine scale structures such as steep moving fronts and emerging steep layers, pulses, shocks, etc. In two space dimensions, however, application of moving-grid methods is less trivial than in 1D. For some methods, e.g. those based on equidistributing principles, it is not even clear how to extend the underlying grid selection procedure to 2D. The moving-finite-element (MFE) method does not suffer from this drawback; its mathematical extension to 2D is trivial. However, because of the intrinsic coupling between the discretization of the PDE and the grid selection, the application of MFE, as for any other method, is not without difficulties. In this paper we describe the node movement induced by MFE for various PDEs and we indicate some problems concerning the grid structure that can result from this movement.
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