High-order Unfitted Discretizations for Partial Differential Equations Coupled with Geometric Flow

Lou, Yimin

dc.contributor.advisor	Lehrenfeld, Christoph Prof. Dr.
dc.contributor.author	Lou, Yimin
dc.date.accessioned	2023-02-17T10:13:04Z
dc.date.available	2023-02-24T00:50:09Z
dc.date.issued	2023-02-17
dc.identifier.uri	http://resolver.sub.uni-goettingen.de/purl?ediss-11858/14523
dc.identifier.uri	http://dx.doi.org/10.53846/goediss-9736
dc.format.extent	198 Seiten	de
dc.language.iso	eng	de
dc.rights.uri	http://creativecommons.org/licenses/by/4.0/
dc.subject.ddc	510	de
dc.title	High-order Unfitted Discretizations for Partial Differential Equations Coupled with Geometric Flow	de
dc.type	doctoralThesis	de
dc.contributor.referee	Lehrenfeld, Christoph Prof. Dr.
dc.date.examination	2022-02-18	de
dc.description.abstracteng	We consider a moving free boundary problem where a diffusion equation posed on an evolving domain bounded by a smooth surface is coupled with a mean curvature flow of the bounding surface. The evolution velocity of the geometry is not a priori known but has to be determined, as a part of the problem, by the solution to the diffusion equation and the mean curvature vector of the surface. We develop and analyze new geometrically unfitted discretization methods for solving the diffusion equation and a geometric equation of the mean curvature vector at provable high orders of accuracy. We test the methods with numerical experiments which show convergence rates predicted by our a priori error estimates. With a level set function implicitly representing the geometry, we solve an advection equation of the level set domain transported by a velocity field extended from the surface. To this end, we propose two velocity extension methods and take advantage of a high-order numerical method for hyperbolic conservation laws. By unfolding the geometrically coupled bulk-surface model into three sub-models solved using the methods, we conduct proof-of-concept numerical simulations of this solution-curvature-driven moving free boundary problem.	de
dc.contributor.coReferee	Lube, Gert Prof. Dr.
dc.subject.eng	geometric flow	de
dc.subject.eng	unfitted finite element method	de
dc.subject.eng	mean curvature flow	de
dc.subject.eng	coupled bulk-surface model	de
dc.subject.eng	osmosis model	de
dc.subject.eng	geometric partial differential equation	de
dc.subject.eng	isoparametric finite element method	de
dc.subject.eng	moving free boundary problem	de
dc.identifier.urn	urn:nbn:de:gbv:7-ediss-14523-2
dc.affiliation.institute	Fakultät für Mathematik und Informatik	de
dc.subject.gokfull	Mathematics (PPN61756535X)	de
dc.description.embargoed	2023-02-24	de
dc.identifier.ppn	1837040605
dc.notes.confirmationsent	Confirmation sent 2023-02-17T10:15:01	de

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