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Keywords
(10)
Convergence Rate
Convex Polygon
Elliptic Boundary Value Problem
Finite Element
Mesh Optimization
Mesh Refinement
Optimal Convergence Rate
sobolev space
navierstokes equation
navier stokes
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The optimal convergence rate of a C
The optimal convergence rate of a C,10.1016/j.cam.2009.11.020,Journal of Computational and Applied Mathematics,Ana Maria Soane,Manil Suri,Rouben Rosta
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The optimal convergence rate of a C
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Ana Maria Soane
,
Manil Suri
,
Rouben Rostamian
We establish optimal (up to arbitrary ε>0) convergence rates for a
finite element
formulation of a model
second order
elliptic boundary value problem
in a weightedH2
Sobolev space
with 5th degree Argyris elements. This formulation arises while generalizing to the case of nonsmooth domains an unconditionally stable scheme developed by Liu et al. [J.G. Liu, J. Liu, R.L. Pego, Stability and convergence of efficient Navier–Stokes solvers via a commutator estimate, Comm. Pure Appl. Math. 60 (2007) pp. 1443–1487] for the Navier–Stokes equations. We prove the optimality for both quasiuniform and graded mesh refinements, and provide numerical results that agree with our theoretical predictions.
Journal:
Journal of Computational and Applied Mathematics  J COMPUT APPL MATH
, vol. 233, no. 10, pp. 27112723, 2010
DOI:
10.1016/j.cam.2009.11.020
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References
(6)
Stability and convergence of efficient NavierStokes solvers via a commutator estimate
(
Citations: 15
)
JianGuo Liu
,
Jie Liu
,
Robert L. Pego
Journal:
Communications on Pure and Applied Mathematics  COMMUN PURE APPL MATH
, vol. 60, no. 10, pp. 14431487, 2007
Graded Mesh Refinement and Error Estimates for Finite Element Solutions of Elliptic Boundary Value Problems in Nonsmooth Domains
(
Citations: 30
)
Thomas Apel
,
AnnaMargarete Sändig
,
John R. Whiteman
Journal:
Mathematical Methods in The Applied Sciences  MATH METH APPL SCI
, vol. 19, no. 1, pp. 6385, 1996
Direct and inverse error estimates for finite elements with mesh refinements
(
Citations: 65
)
I. Babuska
,
R. B. Kellogg
,
J. Pitkaeranta
Published in 1979.
Finite Element Approximations in a NonLipschitz Domain
(
Citations: 4
)
Gabriel Acosta
,
María G. Armentano
,
Ricardo G. Durán
,
Ariel L. Lombardi
Published in 2007.
Improving the rate of convergence of ‘high order finite elements’ on polygons and domains with cusps
(
Citations: 27
)
Constantin Băcuţă
,
Victor Nistor
,
Ludmil T. Zikatanov
Journal:
Numerische Mathematik  NUMER MATH
, vol. 100, no. 2, pp. 165184, 2005