Least squares moving finite elements (Q2748863)

The paper describes an extension of the moving finite element (MFE) method for steady-state pure convection problems, namely the least squares MFE method (LSMFE). By the direct treatment of the steady-state problem together with the minimization of a suitable residual functional, the LSMFE method ensures that the nodal points are not transported downstream as by the MFE method rendering the latter one useless for the mentioned class of problems. The constructed method is validated by numerical results in one and two spatial dimensions, showing also greater accuracy than the corresponding fixed node least squares results.