The Gradient Superconvergence of Bilinear Finite Volume Element for Elliptic Problems. Issue 4 (17th November 2016)

• Record Type: Journal Article
• Authors: Zhang, Tie; Tang, Lixin
• Is Part Of: Numerical mathematics. Volume 9:Issue 4(2016)
• Page Start: 579
• Page End: 594
• Publication Date: 2016-11-17
• Subjects: 65N30, -- 65M60; Bilinear finite volume element, -- elliptic problem, -- gradient approximation, -- superconvergence; Numerical analysis -- Periodicals; Numerical analysis; Periodicals; 518.05
• DOI: 10.4208/nmtma.2016.m1515
• Languages: English
• ISSNs: 1004-8979

Abstract

Abstract: We study the gradient superconvergence of bilinear finite volume element (FVE) solving the elliptic problems. First, a superclose weak estimate is established for the bilinear form of the FVE method. Then, we prove that the gradient approximation of the FVE solution has the superconvergence property: where denotes the average gradient on elements containing point P and S is the set of optimal stress points composed of the mesh points, the midpoints of edges and the centers of elements.