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

We establish optimal (up to arbitrary epsilon > 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 (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. (C) 2009 Elsevier B.V. All rights reserved.