Superconvergence analysis of splitting positive definite nonconforming mixed finite element method for pseudo-hyperbolic equations

Abstract

In this paper, a new splitting positive definite nonconforming mixed finite element method is proposed for pseudo-hyperbolic equations, in which a quasi-Wilson quadrilateral element is used for the flux p, and the bilinear element is used for u. Superconvergence results in ‖ · ‖div,h norm for p and optimal error estimates in L2 norm for u are derived for both semi-discrete and fully discrete schemes under almost uniform meshes.