The optimal convergence rate of a C1 finite element method for non-smooth domains

Authors:
Ana Maria Soane;Manil Suri;Rouben Rostamian
Affiliations:
MOX, Dipartimento di Matematica "F. Brioschi", Politecnico di Milano, Via Bonardi 9, 20133 Milano, Italy;Department of Mathematics and Statistics, University of Maryland, Baltimore County (UMBC), Baltimore, MD 21250, USA;Department of Mathematics and Statistics, University of Maryland, Baltimore County (UMBC), Baltimore, MD 21250, USA
Venue:
Journal of Computational and Applied Mathematics
Year:
2010

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Abstract

We establish optimal (up to arbitrary @e0) convergence rates for a finite element formulation of a model second order elliptic boundary value problem in a weightedH^2 Sobolev space with 5th degree Argyris elements. This formulation arises while generalizing to the case of non-smooth 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.