✦ LIBER ✦

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

✍ Scribed by Ana Maria Soane; Manil Suri; Rouben Rostamian

Publisher: Elsevier Science
Year: 2010
Tongue: English
Weight: 925 KB
Volume: 233
Category: Article
ISSN: 0377-0427
DOI: 10.1016/j.cam.2009.11.020

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✦ Synopsis

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 weighted H 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 (2007Math. 60 ( ) pp. 1443Math. 60 ( -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.

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