Transmission problems and domain decompositions for non-autonomous parabolic equations on evolving domains
Alphonse, Amal ; Djurdjevac, Ana ; Engström, Emil LU and Hansen, Eskil LU
(2026)
In Interfaces and Free Boundaries
- Abstract
- Parabolic equations on evolving domains model a multitude of applications including various industrial processes, such as the molding of heated materials. Such equations are numerically challenging as they require large-scale computations and the usage of parallel hardware. Domain decomposition is a common choice of numerical method for stationary domains, as it gives rise to parallel discretizations. In this study, we introduce a variational framework that extends the use of such methods to evolving domains. In particular, we prove that transmission problems on evolving domains are well posed and equivalent to the corresponding parabolic problems. This in turn implies that the standard non-overlapping domain decompositions, including the... (More)
- Parabolic equations on evolving domains model a multitude of applications including various industrial processes, such as the molding of heated materials. Such equations are numerically challenging as they require large-scale computations and the usage of parallel hardware. Domain decomposition is a common choice of numerical method for stationary domains, as it gives rise to parallel discretizations. In this study, we introduce a variational framework that extends the use of such methods to evolving domains. In particular, we prove that transmission problems on evolving domains are well posed and equivalent to the corresponding parabolic problems. This in turn implies that the standard non-overlapping domain decompositions, including the Robin–Robin method, become well-defined approximations. Furthermore, we prove the convergence of the Robin–Robin method. The framework is based on a generalization of fractional Sobolev–Bochner spaces on evolving domains, time-dependent Steklov–Poincaré operators, and elements of the approximation theory for monotone maps. (Less)
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/1346087b-60e9-457b-b9bc-d2097abb01b1
- author
- Alphonse, Amal
; Djurdjevac, Ana
; Engström, Emil
LU
and Hansen, Eskil
LU
- organization
- publishing date
- 2026-03-03
- type
- Contribution to journal
- publication status
- published
- subject
- in
- Interfaces and Free Boundaries
- pages
- 41 pages
- publisher
- European Mathematical Society Publishing House
- ISSN
- 1463-9963
- DOI
- 10.4171/ifb/564
- project
- Moving domain decomposition methods for parabolic PDEs
- language
- English
- LU publication?
- yes
- id
- 1346087b-60e9-457b-b9bc-d2097abb01b1
- date added to LUP
- 2026-03-10 09:40:28
- date last changed
- 2026-07-02 08:31:02
@article{1346087b-60e9-457b-b9bc-d2097abb01b1,
abstract = {{Parabolic equations on evolving domains model a multitude of applications including various industrial processes, such as the molding of heated materials. Such equations are numerically challenging as they require large-scale computations and the usage of parallel hardware. Domain decomposition is a common choice of numerical method for stationary domains, as it gives rise to parallel discretizations. In this study, we introduce a variational framework that extends the use of such methods to evolving domains. In particular, we prove that transmission problems on evolving domains are well posed and equivalent to the corresponding parabolic problems. This in turn implies that the standard non-overlapping domain decompositions, including the Robin–Robin method, become well-defined approximations. Furthermore, we prove the convergence of the Robin–Robin method. The framework is based on a generalization of fractional Sobolev–Bochner spaces on evolving domains, time-dependent Steklov–Poincaré operators, and elements of the approximation theory for monotone maps.}},
author = {{Alphonse, Amal and Djurdjevac, Ana and Engström, Emil and Hansen, Eskil}},
issn = {{1463-9963}},
language = {{eng}},
month = {{03}},
publisher = {{European Mathematical Society Publishing House}},
series = {{Interfaces and Free Boundaries}},
title = {{Transmission problems and domain decompositions for non-autonomous parabolic equations on evolving domains}},
url = {{http://dx.doi.org/10.4171/ifb/564}},
doi = {{10.4171/ifb/564}},
year = {{2026}},
}