We present in this paper a proof of well-posedness and convergence for the parallel Schwarz Waveform Relaxation Algorithm adapted to an N-dimensional semilinear heat equation. Since the equation we study is an evolution one, each subproblem at each step has its own local existence time, we then determine a common existence time for every problem in any subdomain at any step. We also introduce a new technique: Exponential Decay Error Estimates, to prove the convergence of the Schwarz Methods, with multisubdomains, and then apply it to our problem.
@article{M2AN_2014__48_3_795_0,
author = {Tran, Minh-Binh},
title = {Parallel Schwarz Waveform Relaxation Algorithm for an N-dimensional semilinear heat equation},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
volume = {48},
year = {2014},
pages = {795-813},
doi = {10.1051/m2an/2013121},
mrnumber = {3264335},
language = {en},
url = {http://dml.mathdoc.fr/item/M2AN_2014__48_3_795_0}
}
Tran, Minh-Binh. Parallel Schwarz Waveform Relaxation Algorithm for an N-dimensional semilinear heat equation. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Tome 48 (2014) pp. 795-813. doi : 10.1051/m2an/2013121. http://gdmltest.u-ga.fr/item/M2AN_2014__48_3_795_0/
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