Calculating div(grad(u)) and a line integral from pde solution

Dear experts,

I imported a solution of -div(grad(u))=f(u) from the pde app. I would like to do 2 things:

1. re-calculate d^2u/dx^2+d^2u/dy^2 for checking the solution

2. calculate an integral of form int g(u,du/dx,du/dy) dy along a line where x=0.

For both of these tasks, the (brute force) solutions I came up with utilizes pdegrad, tri2grid and pdeprtni a lot.

For 1. I calculate the derivatives with pdegrad, map solution to nodes with pdeprtni and pdegrad again.

For 2. I calculate derivatives with pdegrad, map to square mesh with tri2grid and integrate with trapz.

Unfortunately, all this estimation introduces error. Can anyone suggest a more straightforward & accurate way of doing this?

Thanks!

 Can anyone suggest a more strayou suggest

[Siddharth Sundar]

-Is there a reason you are comparing the two numerical solutions?

-What is the magnitude of error introduced at every step of the calculation?

-Did you try refining the mesh further before exporting the solution to MATLAB? That might help.

-You could try integral2 instead of trapz and see if that helps.

[Hanne]

-Is there a reason you are comparing the two numerical solutions?

This is the first time I'm using pde toolbox so just wanted to see whether I defined the equation correctly.

-What is the magnitude of error introduced at every step of the calculation?

I have no idea, for now, the error seems quite small.

-Did you try refining the mesh further before exporting the solution to MATLAB? That might help

Yes, the solution didn't change much. This is the reason I think the magnitude of error isn't too large.

-You could try integral2 instead of trapz and see if that helps.

I did play around with this. I cound't figure out how to properly import the numerical data vectors u,du/dx,du/dy into integral2, but I'll take another look. Thanks for the tip!