where is the unity tensor and .

The calculation of the gradients of the weight functions of even order is straightforward:

(2.57) | ||

(2.58) | ||

(2.59) |

The calculation of the gradients of the weight functions of odd order takes into account that eqns. (2.49) to (2.51) all have the same functional form,

(2.60) |

Applying the product rule and using eqns. (2.55) and (2.56) yields

(2.61) | ||||

(2.62) | ||||

(2.63) |

The derivatives are readily obtained

(2.64) | ||||

(2.65) | ||||

(2.66) |

which finally allows the gradients of the odd weight functions to be written as

(2.67) | ||

(2.68) | ||

(2.69) |