Volume 32, pp. 173-189, 2008.

Numerical analysis of Stokes equations with improved LBB dependency

M. Wohlmuth and M. Dobrowolski

Abstract

We provide a-priori bounds with improved domain dependency for the solution of Stokes equations and the numerical error of an approximation by conforming finite element methods. The domain dependency appears primarily in terms of the LBB-constant $L$, and several previous works have shown that $L$ degenerates with the aspect ratio of the domain. We explain the LBB dependency of common a-priori bounds on $Du$ and $p$ and improve most of these estimates by avoiding a global inf-sup condition and assuming locally-balanced flow, which is in particular satisfied if $g=0$. In this case, all error bounds on $u-u_h$ and $p-p_h$, except for $\|p-p_h\|[L^2(\Omega)],$ prove to be completely independent of $L$.

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Key words

LBB-constant, inf-sup condition, Stokes equations, a-priori estimates, finite elements

AMS subject classifications

65N30, 76D07

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