A new low order least squares nonconforming characteristics mixed finite element method For Burgers’ equation

In this paper, a new low order least squares nonconforming characteristics mixed finite element method (MFEM) is considered for two-dimensional Burgers’ equation. By use of two typical characters of the elements for approximating the velocity and flux variables: (a) the consistency errors of the elements can be estimated as order O(h2)O(h2) with respect to the mesh size h   in the broken H1H1-norm, one order higher than their interpolation errors; (b) the elements’ interpolation operators satisfy certain orthogonalities, which lead to O(h2)O(h2) order error estimates in L2L2-norm and some superclose results, the accuracy of corresponding variables in L2L2-norm is improved by one order compared with other MFEMs in the existing literature. It seems that the results provided herein have never been derived before.