Energy Stability and Convergence of SAV Block-centered Finite Difference Method for Gradient Flows
For researchers in numerical analysis and computational PDEs, this work provides a rigorous theoretical foundation for a high-order, efficient scheme for gradient flows.
The paper develops a block-centered finite difference method for the scalar auxiliary variable Crank-Nicolson scheme (SAV/CN-BCFD) for gradient flows, proving second-order accuracy in time and space. Numerical experiments on Allen-Cahn and Cahn-Hilliard equations confirm robustness and efficiency.
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.