I am using backward Euler in a FEM scheme for a convection-diffusion problem. On a given mesh, I can take arbitrarily large time steps, as expected. But if I decrease time step, at some point it will generate oscillations in the solution (spikes). Is this a known behavior? It's not mentioned in text books, at least the ones I know. Would CrankNicolson scheme eliminate the issue?The above mentioned problem is only the simplest one to demonstrate the phenomenon. I attach an image of what is happening in my real problem: transient (here only 2D) incompressible flow. $\rho=1$, dynamic $\eta=1\times 10^{-3}$, flat inflow 1, cylinder diameter 0.1 ($R_e=100$). If timestep is 0.0001, such oscillations occur. If timestep is 0.005, solution becomes smooth and I reproduce von Karman vortices with proper frequency, so it is highly unlikely I have a bug in the code.This is standard Galerkin FEM with no stabilization solved with a direct solver.Any other thoughts how this is possible and how to know how small timestep is too small.Thanks for any hints.Dominik
Solution oscillations with a small timestep in backward Euler
pde;finite element;stability;fem