```Date: Jul 8, 2013 10:47 AM
Author: Steven Finch
Subject: pdenonlin "Stepsize too small"

Please download two files ellipseb2.m & ellipseg.m from http://www.people.fas.harvard.edu/~sfinch/matlab/and execute the following code:g='ellipseg';b='ellipseb2';c='1./sqrt(1+ux.^2+uy.^2)';a=0;f=0;rtol=1e-4;[p,e,t]=initmesh(g);[p,e,t]=refinemesh(g,p,e,t); u=pdenonlin(b,p,e,t,c,a,f,'tol',rtol);figure;pdeplot(p,e,t,'xydata',u,'zdata',u,'mesh','on','colorbar','off');axis equal tight;format long[ux,uy]=pdegrad(p,t,u);tArea = pdetrg(p,t);surfaceArea = sqrt(1 + ux.^2 + uy.^2)*tArea';surfaceArea[p,e,t]=refinemesh(g,p,e,t);u=pdenonlin(b,p,e,t,c,a,f,'tol',rtol);[ux,uy]=pdegrad(p,t,u);tArea = pdetrg(p,t);surfaceArea = sqrt(1 + ux.^2 + uy.^2)*tArea';surfaceAreaEverything works fine up to this point.  The graph shows the minimal surface spanning a folded circular loop (with sharp corners at two boundary points).  A good numerical estimate 2.48201... is found (the true value is 2.48228...).  If, however, we attempt to improve upon the estimate via[p,e,t]=refinemesh(g,p,e,t);u=pdenonlin(b,p,e,t,c,a,f,'tol',rtol);then the following message appears:??? Error using ==> pdenonlin at 251Stepsize too small. Does anyone have suggestions for how to avoid this problem?  Thank you,Steve Finch P.S.  The two files were created using the command:pdeellip(0,0,1,1/sqrt(2),0)then specifying u = abs(y) using the Boundary Mode menu, and finally using the commands:fid = wgeom(g, 'ellipseg');fid = wbound(b, 'ellipseb2');
```