A coupling method based on new MFE and FE for fourth-order parabolic equation

Abstract

In this article, a coupling method of new mixed finite element (MFE) and finite element (FE) is proposed and analyzed for fourth-order parabolic partial differential equation. First, the fourth-order parabolic equation is split into the coupled system of second-order equations. Then, an equation is solved by finite element method, the other equation is approximated by the new mixed finite element method, whose flux belongs to the square integrable space replacing the classical H(div;Ω) space. The stability for fully discrete scheme is derived, and both semi-discrete and fully discrete error estimates are obtained. Moreover, the optimal a priori error estimates in L 2 and H 1-norm for both the scalar unknown u and the diffusion term γ and a priori error estimate in (L 2)2-norm for its flux σ are derived. Finally, some numerical results are provided to validate our theoretical analysis.