Abstract
A low order anisotropic nonconforming rectangular finite element method for the convection–diffusion problem with a modified characteristic finite element scheme is studied in this paper. The O ( h 2 ) order error estimate in L 2 -norm with respect to the space, one order higher than the expanded characteristic-mixed finite element scheme with order O ( h ) , and the same as the conforming case for a modified characteristic finite element scheme under regular meshes, is obtained by use of some distinct properties of the interpolation operator and the mean value technique, instead of the so-called elliptic projection, which is an indispensable tool in the convergence analysis of the previous literature. Lastly, some numerical results of the element are provided to verify our theoretical analysis.
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