dc.contributor.author
Hinrichsen-Bischoff, Jes Lasse
dc.date.accessioned
2023-02-20T11:11:15Z
dc.date.available
2023-02-20T11:11:15Z
dc.identifier.uri
https://refubium.fu-berlin.de/handle/fub188/37844
dc.identifier.uri
http://dx.doi.org/10.17169/refubium-37557
dc.description.abstract
Solutions of variational inequalities often have limited regularity. In particular, the nonsmooth parts are local, while other parts of the solution have higher regularity. To overcome this limitation, we apply hp-adaptivity, which uses a combination of locally finer meshes and varying polynomial degrees to separate the different features of the the solution. For this, we employ Discontinuous Galerkin (DG) methods and show some novel error estimates for the obstacle problem which emphasize the use in hp-adaptive algorithms.
Besides this analysis, we present how to efficiently compute numerical solutions using error estimators, fast algebraic solvers which can also be employed in a parallel setup, and discuss implementation details.
Finally, some numerical examples and applications to phase field models are presented.
dc.format.extent
157 Seiten
dc.rights.uri
http://www.fu-berlin.de/sites/refubium/rechtliches/Nutzungsbedingungen
dc.subject
Discontinuous Galerkin
en
dc.subject
Variational Inequalities
en
dc.subject
Obstacle Problems
en
dc.subject.ddc
500 Naturwissenschaften und Mathematik::510 Mathematik::518 Numerische Analysis
dc.title
Adaptive Discontinuous Galerkin Methods for Variational Inequalities with Applications to Phase Field Models
dc.contributor.gender
male
dc.contributor.firstReferee
Gräser, Carsten
dc.contributor.furtherReferee
Sander, Oliver
dc.date.accepted
2023-01-06
dc.identifier.urn
urn:nbn:de:kobv:188-refubium-37844-1
refubium.affiliation
Mathematik und Informatik
dcterms.accessRights.dnb
free
dcterms.accessRights.openaire
open access