I am trying to solve three coupled non-linear heat equations $A$, $B$ and $C$ using the Galerkin-method and the Newton-method. Now I noticed the following:
- When just solving each equation separately, the method works fine, and converges fast
- When solving the equations $A$ and $C$ together, or $B$ and $C$, the method works fine, and it converges in a reasonable rate (though slower than if just solving one equation)
- When trying to solve the equations $A$ and $B$ together, or all three equations at once, no convergence can be achieved, even for different
I try to find an explanation for that behaviour, but I could not come up with a satisfying yet. It could be that the combination of $A$ and $B$ leads to an unstable system. Are there other possibilities?