Block-centred finite difference methods on rectangular composite grids with refinement in space for parabolic equation

ABSTRACT

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 $(\mathrm{\Delta }t+h^{3/2})$ for simple approximation scheme and of order $(\mathrm{\Delta }t+h^2)$ for more accurate approximation scheme. Numerical experiments using these two schemes show that the convergence rates are in agreement with the theoretical analysis.

KEYWORDS:

• Block-centred finite difference method
• local refinement
• slave node
• piecewise interpolation
• numerical analysis

2010 AMS SUBJECT CLASSIFICATIONS:

• 65M06
• 65M12
• 65M50

Disclosure statement

No potential conflict of interest was reported by the author.

Additional information

Funding

This work is supported by A Project of Shandong Province Higher Educational Science and Technology Program Grant No. J16LI54