Finite Element Analysis for bulk–surface Partial Differential Equations in evolving Domains

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Finite Element Analysis for bulk–surface Partial Differential Equations in evolving Domains

Edelmann, Dominik
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Zitierfähiger Link (URI): http://hdl.handle.net/10900/181105
http://nbn-resolving.org/urn:nbn:de:bsz:21-dspace-1811052
http://dx.doi.org/10.15496/publikation-122429
Dokumentart: Dissertation
Erscheinungsdatum: 2026-06-25
Sprache: Englisch
Fakultät: 7 Mathematisch-Naturwissenschaftliche Fakultät
Fachbereich: Mathematik
Gutachter: Lubich, Christian (Prof. Dr.)
Tag der mündl. Prüfung: 2024-07-10
DDC-Klassifikation: 510 - Mathematik
Schlagworte: Numerische Mathematik , Analysis
Freie Schlagwörter: Finite Elemente
partielle Differentialgleichung
Tumor-Modell
tumor model
partial differential equation
Finite Elements
Lizenz: http://tobias-lib.uni-tuebingen.de/doku/lic_ohne_pod.php?la=de http://tobias-lib.uni-tuebingen.de/doku/lic_ohne_pod.php?la=en
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Abstract:

This dissertation studies the numerical approximation of various partial bulk–surface differential equations in time-dependent domains. The main interest is an application to a model of tissue growth which is a slight modification of a model presented by Eyles, King & Styles [2019]. The model couples a Poisson equation in the time-dependent domain with a forced mean curvature flow of the free boundary surface, with nontrivial bulk–surface coupling in both the velocity law of the evolving boundary surface and the boundary condition of the Poisson equation.

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