The p method of analysis, when used with shape optimization, has certa
in advantages over the h method. The method of h adaptivity results in
fine meshes with small elements in areas of stress concentration. The
presence of these small elements prevents the shape from changing sig
nificantly during optimization due to mesh distortion. The p-adaptive
method uses relatively large sized elements, and adaptivity is achieve
d by increasing the polynomial order of the shape functions rather tha
n by introducing small elements as in the h method. Thus, the p-adapti
ve method allows for greater shape changes without sacrificing the acc
uracy of the analysis. A methodology is developed in this paper to int
egrate p-adaptive analysis with shape optimization for general velocit
y fields. The key contributions lie in an easily implementable shape u
pdate strategy and an adaptive scheme to locally increase the polynomi
al order based on error indicators. Numerical results show that signif
icant shape change is achievable prior to serious mesh distortion, In
addition, need for an h-p adaptive strategy rather than a pure p-adapt
ive strategy is also highlighted.