Solving PDE system in Matlab: Derivatives on a mesh -

i using matlab solve system of coupled pdes, pdenonlin.

i create mesh geometry (a square box circular hole in middle), , refine until :

[p,e,t] = initmesh('defectgeom2'); [p,e,t] = refinemesh('defectgeom2',p,e,t); 

i solve system

% solution: u = pdenonlin(b_s,p,e,t,c_s,a_s,f_s);  % extract different functions full solutions (systems): np = size(p,2); % number of node points uk = reshape(u,np,[]); % each uk column has 1 component of u 

therefore have uk (in case 3) solutions.

now want calculate integrals , derivatives of approximate solutions. tried interpolating uniform grid using tri2grid:

x=linspace(-1,1,npts); y=x;  psi=tri2grid(p,t,uk(:,3),x,y); theta=tri2grid(p,t,uk(:,1),x,y); theta_y=derivative(theta,1,2); psi_x=derivative(psi,1,1); 

and calculate:

pressure = trapz(x,psi_x-cos(2*theta).*theta_y+sin(2*theta)); 

but gives me poor approximation, guess because of fact grid uniform whereas mesh finer around central circle , coarser elsewhere.

is there way use matlab built-in functions calculate derivatives of solutions of pdenonlin without brutally interpolate tri2grid on uniform grid?

there pdeinterpolant class in pde toolbox might useful. use meshtopet generate input arguments mesh , evaluate query interpolant.

you can specify different grid when query interpolant if use finer grid stage might better results without having alter original mesh.