On supraconvergence phenomenon for second order centered finite differences on non-uniform grids

作者：

Highlights：

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• Construction of adaptive grids for BVPs is deeply analyzed.

• It is shown that local mesh refinement does not necessarily lead to low numerical error.

• The stability and convergence of the scheme on non-uniform grids are proved.

• We demonstrate how a 2nd order finite difference scheme can become of the fourth order.

摘要

•Construction of adaptive grids for BVPs is deeply analyzed.•It is shown that local mesh refinement does not necessarily lead to low numerical error.•The stability and convergence of the scheme on non-uniform grids are proved.•We demonstrate how a 2nd order finite difference scheme can become of the fourth order.

论文关键词：primary,65N06,secondary,76M20,65L10,Finite differences,Non-uniform grids,Boundary layer,Boundary value problems,Supraconvergence

论文评审过程：Received 8 November 2016, Revised 9 April 2017, Available online 15 May 2017, Version of Record 29 May 2017.

论文官网地址：https://doi.org/10.1016/j.cam.2017.05.006