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Media type:
E-Article
Title:
Error estimates for a splitting integrator for abstract semilinear boundary coupled systems
Contributor:
Csomós, Petra;
Farkas, Bálint;
Kovács, Balázs
imprint:
Oxford University Press (OUP), 2023
Published in:
IMA Journal of Numerical Analysis, 43 (2023) 6, Seite 3628-3655
Language:
English
DOI:
10.1093/imanum/drac079
ISSN:
0272-4979;
1464-3642
Origination:
Footnote:
Description:
<jats:title>Abstract</jats:title>
<jats:p>We derive a numerical method, based on operator splitting, to abstract parabolic semilinear boundary coupled systems. The method decouples the linear components that describe the coupling and the dynamics in the abstract bulk- and surface-spaces, and treats the nonlinear terms similarly to an exponential integrator. The convergence proof is based on estimates for a recursive formulation of the error, using the parabolic smoothing property of analytic semigroups, and a careful comparison of the exact and approximate flows. This analysis also requires a deep understanding of the effects of the Dirichlet operator (the abstract version of the harmonic extension operator), which is essential for the stable coupling in our method. Numerical experiments, including problems with dynamic boundary conditions, reporting on convergence rates are presented.</jats:p>