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dc.contributor.authorLi, Jichun
dc.contributor.authorSun, Shuyu
dc.date.accessioned2015-08-12T09:31:23Z
dc.date.available2015-08-12T09:31:23Z
dc.date.issued2014-12-02
dc.identifier.citationLi, J., & Sun, S. (2014). The Superconvergence Phenomenon and Proof of the MAC Scheme for the Stokes Equations on Non-uniform Rectangular Meshes. Journal of Scientific Computing, 65(1), 341–362. doi:10.1007/s10915-014-9963-5
dc.identifier.issn08857474
dc.identifier.doi10.1007/s10915-014-9963-5
dc.identifier.urihttp://hdl.handle.net/10754/566180
dc.description.abstractFor decades, the widely used finite difference method on staggered grids, also known as the marker and cell (MAC) method, has been one of the simplest and most effective numerical schemes for solving the Stokes equations and Navier–Stokes equations. Its superconvergence on uniform meshes has been observed by Nicolaides (SIAM J Numer Anal 29(6):1579–1591, 1992), but the rigorous proof is never given. Its behavior on non-uniform grids is not well studied, since most publications only consider uniform grids. In this work, we develop the MAC scheme on non-uniform rectangular meshes, and for the first time we theoretically prove that the superconvergence phenomenon (i.e., second order convergence in the (Formula presented.) norm for both velocity and pressure) holds true for the MAC method on non-uniform rectangular meshes. With a careful and accurate analysis of various sources of errors, we observe that even though the local truncation errors are only first order in terms of mesh size, the global errors after summation are second order due to the amazing cancellation of local errors. This observation leads to the elegant superconvergence analysis even with non-uniform meshes. Numerical results are given to verify our theoretical analysis.
dc.publisherSpringer Nature
dc.subjectMAC scheme
dc.subjectNon-uniform rectangular grids
dc.subjectStaggered grids
dc.subjectStokes equations
dc.titleThe Superconvergence Phenomenon and Proof of the MAC Scheme for the Stokes Equations on Non-uniform Rectangular Meshes
dc.typeArticle
dc.contributor.departmentComputational Transport Phenomena Lab
dc.contributor.departmentEarth Science and Engineering Program
dc.contributor.departmentPhysical Science and Engineering (PSE) Division
dc.identifier.journalJournal of Scientific Computing
dc.contributor.institutionDepartment of Mathematical Sciences, University of Nevada Las VegasLas Vegas, NV, United States
kaust.personSun, Shuyu
dc.date.published-online2014-12-02
dc.date.published-print2015-10


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