  We study the phase mixing and dissipation of a packet of standing shear
Alfv\'en waves localized in a region with non-uniform Alfv\'en background
velocity. We investigate the validity of the exponential damping law in time,
$\exp(-At^3)$, presented by Heyvaerts & Priest (1983) for different ranges of
Lundquist, $S$, and Reynolds, $R$, numbers. Our numerical results shows that it
is valid for $(R,S)\geq 10^7$.
