Least squares moving finite elements

The moving finite element (MFE) method, when applied to purelyhyperbolic partial differential equation, moves nodes with approximatelycharacteristic speeds, which makes the method useless for steady-stateproblems. We introduce the least squares MFE method (LSMFE)for steady-state pure convection problems which corrects thisdefect. We show results for a steady-state pure convection problemin one dimension in which the nodes are no longer swept downstreamas in MFE. The method is then extended to two dimensions andthe grid aligns automatically with the flow, thereby yieldingfar greater accuracy than the corresponding fixed node leastsquares results, as is shown in two-dimensional numerical trials.