I am attempting to solve a modified bessel partial differential equation using a finite element implementation. I have used FDM (with reasonable success) and was hoping to replicate the results using FEM. My exposure to FEM is limited and I was hoping a commercial suite (such as Matlab or Mathematica) could solve this problem. My problem is defined as such -
u(r,t)=0 at t=0 and r=0
du/dr=k1*u(r,t) at r==1 where k1 is a constant
d2u/dr2 +1/r*du/dr - u/r^2 = du/dt +r/2*k2, where k2 is a constant
u and u(r,t) are interchange-able in notation
My question is - is this problem solvable using an FEM toolbox?
Many thanks. RM
Yes the problem can be solved by FEM too. The only thing is that generally the boundary condition at r=0 is ur (0,t) = 0.
Modified Bessel function PDE can be solved with FEM. The boundary conditions should be adequately defined and the application of MATHCAD can be of help. Reference to MATHCAD software tool/guide should be made to direct you. Experts in the use of the tool can help you.
Yes it is possible, you have different ways : first approximate du/dt by using the classical approximation (u^{n+1}(r)-u^n(r))/dt than write the semidiscrete scheme (most famous explicit, implicit scheme). After this write the variational problem and go to FreeFem++ to implement it
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