Hello, everyone Now here is a difficult for me and hope to be helped out. I have got scalar data at every grid point in a Cartesian coordinate and also found the positions of extreme points. The criteria for extreme points is

[S(i)-S(i+1)]*[S(i)-S(i-1)]>0, where i will be in x, y and z 3 directions.

But we want to know more precisely the positions of extreme points so I tried to do interpolation and found some extreme points will dispear with the same criteria. This is due to the effect from no-adjencent points. For example, S(0,0,0) is extreme, then S(1,1,0), S(1,1,1),S(1,-1,0) are no-adjencent.

So I wonder should I also consider these no-adjencent points, or only adjent points(totally they are S(0,0,1),S(0,0,-1),S(1,0,0),S(-1,0,0),S(0,1,0),S(0,-1,0)) for interpolation? Of course, more points considered, more reasonable. But more negative effect will destroy the criteria. How do you think about it?

Great thanks

The extrema may not coincide with any of the grid points. You can try to set up a finite-element interpolation and solve for grad(u)=0 to locate the extrema.

thanks a lot. The finite element interpolation you mentioned is for irregular gird? Because the mesh I used is Cartesian coordinate grid,FE interpolation is still good? How about it if compared with other kind of interpolation, like polynomial, B-spline etc? Thanks