[Libmesh-users] High order geometry and finite volume methods

[Miguel A. S. de T. <sal...@gm...>]

Hi,

I want to solve a simple Poisson equation with a diffusion coefficient, a
simple reaction term and apply Adaptive Mesh Ref (AMR). The problem is that
if the diffusion coefficient is  much smaller than the mesh resolution (as
it can happen before applying AMR), I obtain over and undershoots of the
solution. I need this solution to be stable and not be over 1 or under 0
(bounds from the source term).

One way I was able to achieve this was by implementing a Finite Volume
solver within libMesh. Very easy for simple cartesian geometries. However,
now I need to extend it to non-cartesian geometries that are second order.
I am wondering if there are alternatives in libMesh to solve this
over/undershoot problem for the poisson equation.

Thanks
Miguel