I am interested in finding the average value of a “slice”, where it cuts through the middle of my mesh.
I am aware that FreeFEM allows you to integrate functions over borders using int2D for a 3D mesh or int1D for a 2D mesh. But this integral would be in the interior of the mesh, and would represent a vertical slice.
I have tried something like this, but the error induced is a bit too much due to gradients in my solution.
fespace Ph(Th3, P0); Ph2 chi = (x > -0.01 && x < 0.01 ; // I want the 2D average at x = 0, all values of y, all values of z. real avgProbAtCenter = int3d(Th3)(chi*uh) / int3d(Th3)(chi) ;
If I make the range too small or too large around 0, errors are compounded. Is there a better way to get the 2D integral at just x = 0 instead of a region around it?