Dear all, we always hear about the grid independent solution and one has to increase the number of cells to verify the grid independent solution. What about the discretization scheme and the grid shape (topology)? Should one also check the solution against the grid shape and the discretization scheme?

The term "grid independent solution" states, that the solution of a certain procedure doesn't change, if You increase the number of cells. This includes, that the solution is independent of the grid shape. If You choose another discretization scheme, You change the procedure and You have to check if the solution of this new procedure is still grid independent.

If you are talking about the discretisation methods of the solvers, and you have a mesh and solve it with FEM the solution can often be different than that for an FVM solver. Because one method is independent does not mean another method is.