Abstract:

The anisotropic property of the R-T element with one order is proved based on the anisotropic interpolation theorem and applied to  quasi-linear parabolic problems. The convergence analysis and error estimates are  directly given through an interpolation operator  without Ritz projection, and by use of integral identity, the supercloseness of flux is derived in H(div,Ω)-norm.

Key words: quasi-linear parabolic problems; R-T element; anisotropy; supercloseness