| Abstract: |
| In this talk, we will introduce a first-order in time convex splitting scheme for a nonlocal Cahn-Hilliard-Oono type equation with a transport term and subject to Neumann boundary conditions. The presence of the transport term is not a minor modification, since, for instance, we lose the unconditional stability. However, we will prove the stability of our scheme when the time step is sufficiently small. Furthermore, we will prove the consistency of the scheme and the convergence to the exact solution. Finally we will give numerical simulations which illustrate our theoretical results and demonstrate the performance of our scheme for phase separation as well as for crystal nucleation, with different choices of the interaction kernel. |
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