Article ID Journal Published Year Pages File Type
4641384 Journal of Computational and Applied Mathematics 2010 13 Pages PDF
Abstract

We establish optimal (up to arbitrary ε>0ε>0) convergence rates for a finite element formulation of a model second order elliptic boundary value problem in a weighted  H2H2 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.

Related Topics
Physical Sciences and Engineering Mathematics Applied Mathematics
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