A stabilized mixed finite element method for the biharmonic equation based on biorthogonal systems
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We 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...[Show more]
dc.contributor.author | Lamichhane, Bishnu | |
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dc.date.accessioned | 2015-12-10T22:53:41Z | |
dc.identifier.issn | 0377-0427 | |
dc.identifier.uri | http://hdl.handle.net/1885/59447 | |
dc.description.abstract | We 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.publisher | Elsevier | |
dc.source | Journal of Computational and Applied Mathematics | |
dc.subject | Keywords: 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.title | A stabilized mixed finite element method for the biharmonic equation based on biorthogonal systems | |
dc.type | Journal article | |
local.description.notes | Imported from ARIES | |
local.identifier.citationvolume | 235 | |
dc.date.issued | 2011 | |
local.identifier.absfor | 010399 - Numerical and Computational Mathematics not elsewhere classified | |
local.identifier.ariespublication | f5625xPUB491 | |
local.type.status | Published Version | |
local.contributor.affiliation | Lamichhane, Bishnu, College of Physical and Mathematical Sciences, ANU | |
local.description.embargo | 2037-12-31 | |
local.bibliographicCitation.issue | 17 | |
local.bibliographicCitation.startpage | 115 | |
local.bibliographicCitation.lastpage | 144 | |
local.identifier.doi | 10.1016/j.cam.2011.05.005 | |
dc.date.updated | 2016-02-24T09:26:29Z | |
local.identifier.scopusID | 2-s2.0-79960045393 | |
local.identifier.thomsonID | 000293432300022 | |
Collections | ANU Research Publications |
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