wrupp / nonlinearfem Goto Github PK

Hi,
I would like to see a Matlab code for the Dirichlet boundary condition of the evolution of the two-dimensional heat
equation by finite element method, For example

U_t - div(U)=f(x,y,t) in [0,L][0,L][0,T]
u(.,.,t)= g(.,.,t)=exp(-t)sin(pix)sin(piy) in the boundary [0,T]
U(x,y,0)=Uo [0,L][0,L]

i have code of the generate a triangular grid (mesh) and the assembly of global mass, stiffness matrices and load vector

but the dirichlet boundary conditions according to g and domain [0,L]*[0,L], It's not work in Matlab!

See what i did :

`

[M,A,b]=assembly(p,e,.....);
np=size(p,2);  
x=p(1,:)'; y=p(1,:)';  
bndry=unique([e(1,:) e(2,:)]);
IN= setdiff([1:np])

T=1;  %final time
L=21;
dt=T/L-1; 

U_fem=zeros(np,L);

for k=1:L
    t(k)= (k-1)*dt;
b=b(IN)-A(IN,bndry)*g(x,y,t(k));   
A=A(IN,IN);
M=M(IN,IN);

% solve for FEM solution U_fem

    U_fem(:,1)=sin(pi*x).*sin(pi*y);   % initial condition
    U_fem(bndry,k)= exp(t(k)).*sin(pi*x).*sin(pi*y);  % or =g(x,y,t(k);
    
    U_fem(IN,k+1)= (M+dt*A)/(M*U_fem(IN,k) + dt*b);
    
end

figure()
pdesurf(p,t,U_fem(:,L))

`