Superconvergence analysis of the MAC scheme for the two dimensional stokes problem. Issue 6 (15th April 2016)

• Record Type: Journal Article
• Authors: Lin, Yanping; Zou, Qingsong
• Is Part Of: Numerical methods for partial differential equations. Volume 32:Issue 6(2016:Nov.)
• Page Start: 1647
• Page End: 1666
• Publication Date: 2016-04-15
• Subjects: finite volume element methods -- marker and cell method -- Stokes equations -- superconvergence; Differential equations, Partial -- Numerical solutions -- Periodicals; 515.353
• DOI: 10.1002/num.22066
• Languages: English
• ISSNs: 0749-159X

Abstract

Abstract : This article is concerned with a rigorous superconvergence analysis of the marker and cell method (MAC) for steady Stokes equations. We first derive the MAC scheme from a staggered finite volume element method (FVEM) with a proper quadrature. Then by comparing the MAC to the corresponding FVEM, we prove the superconvergence of the MAC scheme over non‐uniform rectangular meshes. As a byproduct, an optimal order L 2 error estimate is also obtained. © 2016Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 32: 1647–1666, 2016