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

Bernard Bialecki, Maksymilian Dryja, Ryan I. Fernandes

Research output: Contribution to journalArticlepeer-review

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.

Original languageBritish English
Pages (from-to)2757-2784
Number of pages28
JournalMathematics of Computation
Volume90
Issue number332
DOIs
StatePublished - Jan 2021

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