Convergence analysis of the finite difference ADI scheme for the heat equation on a convex set

Bialecki, Bernard; Dryja, Maksymilian; Fernandes, Ryan

doi:10.1090/mcom/3653

Convergence analysis of the finite difference ADI scheme for the heat equation on a convex set
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by Bernard Bialecki, Maksymilian Dryja and Ryan I. Fernandes;

Math. Comp. 90 (2021), 2757-2784

DOI: https://doi.org/10.1090/mcom/3653

Published electronically: July 15, 2021

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Abstract:

It is well known that for the heat equation on a rectangle, the finite difference alternating direction implicit (ADI) method converges with order two. For the first time in the literature, we bound errors of the finite difference ADI method for the heat equation on a convex set for which it is possible to construct a partition consistent with the boundary. Numerical results indicate that the ADI method may also work for some nonconvex sets for which it is possible to construct a partition consistent with the boundary.

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