Dear all:

Is it necessary to evaluate x_{\epilson} for f_{\epsilon} = f_x * x_{\epilson} in numerical grid generation? From the book of Thompson, I found these words:

...It should be understood that there is no incentive, per se, for accuracy in the metrix coefficients, since the object is simply to represent a discrete solution accurately, not to represent the solution on some particular coordinate system. The only reason for using any function at all to define the point distribution is to ensure a smooth distribution. There is no reason that the representations of the coordinate derivatives have to be accurate representations of the analytical derivatives of that particular distribution function.

Excuse me for so long citation. In my understanding, these words told us that one need not to evaluate the coordinate derivatives accurate. Is that so?

From "Numerical grid generation: foundations and applications"

With regards

Zhou

(1). It is perhaps easier to send e-mail to him directly to get some answers.