Non linear elliptic equation, thanks to G. Sadaka
\begin{array}{rcll} \Delta u & =&\nu(u)\cdot u & \mbox{on } \Omega=B(0,R)\subset \mathbb{R}^2\\ u(x,y)&\rightarrow& +\infty &\mbox{on } \partial \Omega \end{array}
download example: Sadaka_Nonlinear_Elliptic.edp or return to 2D examples
verbosity=0.;
real Dx=.02, R=1.;
border C(t=0.,2.*pi){x=R*cos(t);y=R*sin(t);label=1;};
mesh Th=buildmesh(C(floor(2.*pi*R/Dx)));
fespace Vh(Th,P1);
Vh uh, uh0=0, V=uh0, vh;
macro Grad(u)[dx(u),dy(u)]//
real N=2000.;
problem probdup(uh,vh) = - int2d(Th)(Grad(uh)'*Grad(vh))
- int2d(Th) ( uh*V*vh ) + on(1,uh=N);
for (int i=0;i<=1000;i++) {
probdup;
V=uh;
if (i%10==0)
plot(uh,cmm="iter="+i+";min="+uh[].min+";max="+uh[].max+";N="+N,fill=true,value=true,dim=3,
wait=1,boundary=false);
}