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}
}