Higher order multipoint flux mixed finite element methods for parabolic equation

Abstract

In this paper, we consider higher order multipoint flux mixed finite element methods for parabolic problems. The methods are based on enhanced Raviart-Thomas spaces with bubbles. The tensor-product Gauss-Lobatto quadrature rule is employed, which enables local velocity elimination and results in a symmetric, positive definite cell-based system for pressures. We construct two fully discrete schemes for the problems, including the backward Euler scheme and Crank-Nicolson scheme. Theoretical analysis shows optimal order convergence for pressure and velocity on $h^2$-perturbed meshes. Numerical experiments are presented to verify the theoretical results and demonstrate the superiority of the proposed method compared to classical mixed finite element methods.