Convergence and stability of a BSLM for advection-diffusion models with Dirichlet boundary conditions

作者：

Highlights：

• Concrete convergence analysis for a backward semi-Lagrangian method (BSLM) based on finite difference method for non-linear advection-diffusion problems is fully presented.

• The unconditional stability of the BSLM is theoretically shown and also supported by numerical experiments.

摘要

•Concrete convergence analysis for a backward semi-Lagrangian method (BSLM) based on finite difference method for non-linear advection-diffusion problems is fully presented.•The unconditional stability of the BSLM is theoretically shown and also supported by numerical experiments.

论文关键词：Burgers’ equation,Semi-Lagrangian method,Non-linear advection–diffusion equation,Convergence analysis,Stability analysis

论文评审过程：Received 2 November 2018, Revised 6 September 2019, Accepted 9 September 2019, Available online 21 September 2019, Version of Record 21 September 2019.

论文官网地址：https://doi.org/10.1016/j.amc.2019.124744