Hi all, I have been trying to track down a problem for a few days with solving a linear system arising from a finite differenced PDE in spherical coordinates. I found that PETSc managed to converge to a nice solution for my matrix at small grid sizes and everything looks pretty good. But when I try larger more realistic grid sizes, PETSc fails to converge. After trying with another direct solver library, I found that the direct solver found a solution which exactly solves the matrix equation, but when plotting the solution, I see that it oscillates rapidly between the grid points and therefore isn't a satisfactory solution. (At smaller grids the solution is nice and smooth) I was wondering if this phenomenon is common in PDEs? and if there is any way to correct for it? I am currently using 2nd order centered differences for interior grid points, and 1st order forward/backward differences for edge points. Would it be worthwhile to try moving to 4th order differences instead? Or would that make the problem worse? I've even tried smoothing the parameters which go into the matrix entries using moving averages...which doesn't seem to help too much. Any advice from those who have experience with this phenomenon would be greatly appreciated! Thanks, Patrick