Least squares moving finite elements

Miller, K. and Baines, M. J. (2001) Least squares moving finite elements. IMA Journal of Numerical Analysis, 21 (3). pp. 621-642. ISSN 1464-3642 doi: 10.1093/imanum/21.3.621

Abstract/Summary

The moving finite element (MFE) method, when applied to purely hyperbolic partial differential equation, moves nodes with approximately characteristic speeds, which makes the method useless for steady‐state problems. We introduce the least squares MFE method (LSMFE) for steady‐state pure convection problems which corrects this defect. We show results for a steady‐state pure convection problem in one dimension in which the nodes are no longer swept downstream as in MFE. The method is then extended to two dimensions and the grid aligns automatically with the flow, thereby yielding far greater accuracy than the corresponding fixed node least squares results, as is shown in two‐dimensional numerical trials.