English

Energy Stability and Convergence of SAV Block-centered Finite Difference Method for Gradient Flows

Numerical Analysis 2018-12-06 v1

Abstract

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.

Keywords

Cite

@article{arxiv.1812.01793,
  title  = {Energy Stability and Convergence of SAV Block-centered Finite Difference Method for Gradient Flows},
  author = {Xiaoli Li and Jie Shen and Hongxing Rui},
  journal= {arXiv preprint arXiv:1812.01793},
  year   = {2018}
}
R2 v1 2026-06-23T06:32:10.863Z