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A stabilized mixed finite element method for the biharmonic equation based on biorthogonal systems

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dc.contributor.authorLamichhane, Bishnu
dc.date.accessioned2015-12-10T22:53:41Z
dc.date.issued2011
dc.date.updated2016-02-24T09:26:29Z
dc.description.abstractWe propose a stabilized finite element method for the approximation of the biharmonic equation with a clamped boundary condition. The mixed formulation of the biharmonic equation is obtained by introducing the gradient of the solution and a Lagrange multiplier as new unknowns. Working with a pair of bases forming a biorthogonal system, we can easily eliminate the gradient of the solution and the Lagrange multiplier from the saddle point system leading to a positive definite formulation. Using a superconvergence property of a gradient recovery operator, we prove an optimal a priori estimate for the finite element discretization for a class of meshes.
dc.identifier.issn0377-0427
dc.identifier.urihttp://hdl.handle.net/1885/59447
dc.publisherElsevier
dc.sourceJournal of Computational and Applied Mathematics
dc.subjectKeywords: A-priori estimates; Biharmonic equations; Biorthogonal; Clamped plates; Mixed finite element methods; Saddle point problems; Coercive force; Fourier analysis; Frequency multiplying circuits; Lagrange multipliers; Mathematical operators; Finite element met A priori estimate; Biharmonic equation; Biorthogonal system; Clamped plate; Mixed finite element method; Saddle point problem
dc.titleA stabilized mixed finite element method for the biharmonic equation based on biorthogonal systems
dc.typeJournal article
local.bibliographicCitation.issue17
local.bibliographicCitation.lastpage144
local.bibliographicCitation.startpage115
local.contributor.affiliationLamichhane, Bishnu, College of Physical and Mathematical Sciences, ANU
local.contributor.authoruidLamichhane, Bishnu, u4573541
local.description.embargo2037-12-31
local.description.notesImported from ARIES
local.identifier.absfor010399 - Numerical and Computational Mathematics not elsewhere classified
local.identifier.ariespublicationf5625xPUB491
local.identifier.citationvolume235
local.identifier.doi10.1016/j.cam.2011.05.005
local.identifier.scopusID2-s2.0-79960045393
local.identifier.thomsonID000293432300022
local.type.statusPublished Version

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