In my last question I noticed a peculiar error when solving the Poisson equation using finite volume method (FVM), Peculiar error when solving the Poisson equation on a non-uniform mesh (1D only) finite volume method.
This is actually only one equation in coupled system of non-linear equations. The other equations in the system are of advection-reaction-diffusion type which I can solved robustly using a FVM scheme (http://danieljfarrell.github.io/FVM/advection_diffusion.html).
Would it be feasible to use a mixed approach in this case? For example, using a finite difference scheme to solve the Poisson equation and sticking with the FVM for the advection-diffusion equations?
I am using a method of lines (MOL) when solving these equations, so I only need supply a vector which represents the spatial discretisation of each variable. I was hoping that if I use a finite difference method for the Poisson equation I could then interpolate the resulting vector on to the finite volume mesh afterwards?
This might sound like a hack, but wanted to get your opinion before trying it. Maybe moving to a finite element approach is needed?