Quadrilateral Mesh L ~ 2 Projection Superconvergence Analysis

In this paper, we study the symmetric expansion properties of a new quadrilateral finite element ABF_r on the rectangular meshes. For the lowest ABF_r element r = 0,we get h² convergence under u∈(H³(Ω))²∩H₀(div,Ω) through using Bramble-Hilbert lemma and Bilinear lemma, on the other hand, we also present 3-D ABF_r element, and get a petch recovery superconvergence for this element based on the property of keeping optimal convergent error order of the element.