A localisation technique based on radial basis function partition of unity for solving Sobolev equation arising in fluid dynamics

作者：

Highlights：

• The Sobolev equation is the mathematical model of the vertical non stationary groundwater flow with dynamic capillary-pressure effect in a porous medium.

• A new hybrid scheme based LRBF-PUM is formulated to approximate the Sobolev equation.

• The theoretical convergence and unconditional stability of the proposed semi-discrete approach are both analyzed and confirmed numerically.

• The LRBF-PUM method useful for complex domains with acceptable accuracy was proposed.

摘要

•The Sobolev equation is the mathematical model of the vertical non stationary groundwater flow with dynamic capillary-pressure effect in a porous medium.•A new hybrid scheme based LRBF-PUM is formulated to approximate the Sobolev equation.•The theoretical convergence and unconditional stability of the proposed semi-discrete approach are both analyzed and confirmed numerically.•The LRBF-PUM method useful for complex domains with acceptable accuracy was proposed.

论文关键词：Sobolev equation,Finite difference,Local meshless method,RBF,LRBF-PUM,Error estimate

论文评审过程：Received 21 October 2020, Revised 29 January 2021, Accepted 31 January 2021, Available online 22 February 2021, Version of Record 22 February 2021.

论文官网地址：https://doi.org/10.1016/j.amc.2021.126063