In this paper, we present a predictor-corrector type algorithm for solution of linear parabolic problems on graph structure. The graph decomposition is done by dividing some edges and therefore we get a set of problems on sub-graphs, which can be solved efficiently in parallel. The convergence analysis is done by using the energy estimates. It is proved that the proposed finite-difference scheme is unconditionally stable but the predictor step error gives only conditional approximation. In the second part of the paper it is shown that the presented algorithm can be written as Douglas type scheme, based on the domain decomposition method. For a simple case of one dimensional parabolic problem, the convergence analysis is done by using results from [P. Vabishchevich. A substracturing domain decomposition scheme for unsteady problems. Comp. Meth. Appl. Math. 11(2):241-268, 2011]. The optimality of asymptotical error estimates is investigated. Results of computational experiments are presented.
Tumanova, N. (2012). Predictor-corrector domain decomposition algorithm for parabolic problems on graphs. Mathematical Modelling and Analysis, 17(1), 113-127. https://doi.org/10.3846/13926292.2012.645891
Authors who publish with this journal agree to the following terms
that this article contains no violation of any existing copyright or other third party right or any material of a libelous, confidential, or otherwise unlawful nature, and that I will indemnify and keep indemnified the Editor and THE PUBLISHER against all claims and expenses (including legal costs and expenses) arising from any breach of this warranty and the other warranties on my behalf in this agreement;
that I have obtained permission for and acknowledged the source of any illustrations, diagrams or other material included in the article of which I am not the copyright owner.
on behalf of any co-authors, I agree to this work being published in the above named journal, Open Access, and licenced under a Creative Commons Licence, 4.0 https://creativecommons.org/licenses/by/4.0/legalcode. This licence allows for the fullest distribution and re-use of the work for the benefit of scholarly information.
For authors that are not copyright owners in the work (for example government employees), please contact VILNIUS TECHto make alternative agreements.