Energy stability and convergence of SAV block centered finite difference method for gradient flows
We present in this paper construction and analysis of a block centered finite difference method for the spatial discretization of the scalar auxiliary variable Crank Nicolson scheme (SAV/CN BCFD) for gradient flows, and show rigorously that scheme is second order in both time and space in various discrete norms. When equipped with an adaptive time strategy, the SAV/CN BCFD scheme is accurate and extremely efficient. Numerical experiments on typical Allen Cahn and Cahn Hilliard equations are presented to verify our theoretical results and to show the robustness and accuracy of the SAV/CN BCFD scheme.
Math. Comput.