dc.contributor.author
Berninger, Heiko
dc.contributor.author
Sander, Oliver
dc.date.accessioned
2018-06-08T08:07:30Z
dc.date.available
2014-07-16T07:25:17.018Z
dc.identifier.uri
https://refubium.fu-berlin.de/handle/fub188/19394
dc.identifier.uri
http://dx.doi.org/10.17169/refubium-23049
dc.description.abstract
We prove a substructuring result for a variational inequality concerning - but
not restricted to - the Richards equation in homogeneous soil and including
boundary conditions of Signorini's type. This generalizes existing results for
the linear case and leads to interface conditions known from linear
variational equalities: continuity of Dirichlet and flux values in a weak
sense. In case of the Richards equation these are the continuity of the
physical pressure and of the water flux, which is hydrologically reasonable.
Therefore, we also apply these interface conditions in the heterogeneous case
of piecewise constant soil parameters, which we address by the Robin method.
We prove that, for a certain time discretization, the homogeneous problems in
the subdomains including Robin and Signorini-type boundary conditions can be
solved by convex minimization. As a consequence we are able to apply monotone
multigrid in the discrete setting as an efficient and robust solver for the
local problems. Numerical results demonstrate the applicability of our
approach.
de
dc.relation.ispartofseries
urn:nbn:de:kobv:188-fudocsseries000000000226-9
dc.rights.uri
http://www.fu-berlin.de/sites/refubium/rechtliches/Nutzungsbedingungen
dc.subject
Domain decomposition methods
dc.subject
saturated-unsaturated porous media flow
dc.subject
convex minimization
dc.subject
monotone multigrid
dc.subject.ddc
500 Naturwissenschaften und Mathematik::510 Mathematik
dc.title
Substructuring of a Signorini-type problem and Robin's method for the Richards
equation in heterogeneous soil
dcterms.bibliographicCitation.url
http://www.math.fu-berlin.de/publ/preprints/2009/Ab-A-09-03.html
refubium.affiliation
Mathematik und Informatik
de
refubium.affiliation.other
Institut für Mathematik
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refubium.mycore.fudocsId
FUDOCS_document_000000020592
refubium.mycore.reportnumber
A /03/2009
refubium.series.issueNumber
Preprints, Serie A: Mathematik
refubium.series.name
Freie Universität Berlin, Fachbereich Mathematik und Informatik
refubium.series.reportNumber
A /03/2009
refubium.mycore.derivateId
FUDOCS_derivate_000000003699
dcterms.accessRights.openaire
open access