标题：Block-centred finite difference methods on rectangular composite grids with refinement in space for parabolic equation
作者机构：[Liu, W] School of Mathematics, Shandong University, Jinan, China, School of Mathematics and Quantitative Economics, Shandong University of Finance an 更多
通讯作者地址：[Liu, W] School of Mathematics and Quantitative Economics, Shandong University of Finance and EconomicsChina;
来源：International Journal of Computer Mathematics
关键词：65M06; 65M12; 65M50; Block-centred finite difference method; local refinement; numerical analysis; piecewise interpolation; slave node
摘要：Two block-centred finite difference schemes with local refinement in space are introduced and analysed to solve parabolic equation. One scheme is simple approximation scheme, in which piecewise constant interpolation approximation is used for slave nodes. The other is more accurate approximation scheme, with piecewise linear interpolation approximation along the interface. Error estimates in the discrete L 2 norm are derived of order (Δt+h 2 ) for simple approximation scheme and of order (Δt+h 3/2 ) for more accurate approximation scheme. Numerical experiments using these two schemes show that the convergence rates are in agreement with the theoretical analysis. © 2019, © 2019 Informa UK Limited, trading as Taylor & Francis Group.