[gorkemocalan]

Hello,

I am trying to solve heat equation du/dt=\alpha*(d2u/dx2+d2u/dy2)

with boundary conditions u(x,0,t)=0;
u(x,1,t)=(x-x^2)
u(0,y,t)=0;
u(1,y,t)=0;
initial cond. u(x,y,0)=0;

(alpha=0.1)

by using Galerkin FEM(bilenar rectangular=square=4-noded element) with Euler/Implicit/Crank-Nicolson. (41x41 and 81x81 mesh and 4*alpha*dt/dx^2=0.5)

I did coding in MATLAB. It seems OK but I could not perform the analytical solution. Instead of analytical solution of heat equation, I did error analysis considering the analytical solution of laplace equation.

I observed that the error increases in 81x81 mesh. I could not figure out where the mistake/bug is.

Need some help...

Thanks,