Hello,
I am studying several articles and modeling them in Comsol for verification.
The PDE is as follows:
dC/dt= d^2C/dx^2 - alpha* dC/dx (Lloyd and Clements)
and the boundary conditions at both end are;
J(-1,t)=J(0,t)= dC/dx -alpha*C =0
I am employing boundary conditions as a constraint ( -ux + alpha*u)
Initial condition;
C(x,0)=1
When I edit the weak term field in Subdomain settings as:
-ux*test(ux)+alpha*ux*test(u) (A basic reduction with integration by part)
it fails to give matching results with both the article and analytical solutions of this equation.
However another weak form transformation of this equation given by the article linked below:
www.packaging.buffalo.edu/publication/paper2005/lin2005a.pdf
which basically is:
q= dC/dx-alpha*C
dC/dt=nabla(q)
So while integration by part v=q, w=test(u) and the weak form becomes:
-ux*test(ux)+alpha*u*test(ux)
Same boundary and initial conditions. And results match the ones from article and analytical solution.
My question is that is this a result of how Comsol handles weak form equations in ''Weak Form Subdomain'' in PDE Module. Or am I making an embarrassing mistake in terms of mathematics?
Best Regards
I am studying several articles and modeling them in Comsol for verification.
The PDE is as follows:
dC/dt= d^2C/dx^2 - alpha* dC/dx (Lloyd and Clements)
and the boundary conditions at both end are;
J(-1,t)=J(0,t)= dC/dx -alpha*C =0
I am employing boundary conditions as a constraint ( -ux + alpha*u)
Initial condition;
C(x,0)=1
When I edit the weak term field in Subdomain settings as:
-ux*test(ux)+alpha*ux*test(u) (A basic reduction with integration by part)
it fails to give matching results with both the article and analytical solutions of this equation.
However another weak form transformation of this equation given by the article linked below:
www.packaging.buffalo.edu/publication/paper2005/lin2005a.pdf
which basically is:
q= dC/dx-alpha*C
dC/dt=nabla(q)
So while integration by part v=q, w=test(u) and the weak form becomes:
-ux*test(ux)+alpha*u*test(ux)
Same boundary and initial conditions. And results match the ones from article and analytical solution.
My question is that is this a result of how Comsol handles weak form equations in ''Weak Form Subdomain'' in PDE Module. Or am I making an embarrassing mistake in terms of mathematics?
Best Regards