Trace operators of the bi-Laplacian and applications

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dc.contributor.authorFuhrer, Thomas
dc.contributor.authorHaberl, Alexander
dc.contributor.authorHeuer, Norbert
dc.date.accessioned2024-01-10T12:37:01Z
dc.date.available2024-01-10T12:37:01Z
dc.date.issued2021
dc.description.abstractWe study several trace operators and spaces that are related to the bi-Laplacian. They are motivated by the development of ultraweak formulations for the bi-Laplace equation with homogeneous Dirichlet condition, but are also relevant to describe conformity of mixed approximations. Our aim is to have well-posed (ultraweak) formulations that assume low regularity under the condition of an L-2 right-hand side function. We pursue two ways of defining traces and corresponding integration-by-parts formulas. In one case one obtains a nonclosed space. This can be fixed by switching to the Kirchhoff-Love traces from Fiihrer et al. (2019, An ultraweak formulation of the Kirchhoff-Love plate bending model and DPG approximation. Math. Comp., 88, 1587-1619). Using different combinations of trace operators we obtain two well-posed formulations. For both of them we report on numerical experiments with the discontinuous Petrov-Galerkin method and optimal test functions. In this paper we consider two and three space dimensions. However, with the exception of a given counterexample in an appendix (related to the nonclosedness of a trace space) our analysis applies to any space dimension larger than or equal to two.
dc.description.funderComision Nacional de Investigacion Cientifica y Tecnologica (CONICYT) through Fondo Nacional de Desarrollo Cientifico y Tecnologico (FONDECYT)
dc.fechaingreso.objetodigital2024-05-02
dc.format.extent25 páginas
dc.fuente.origenWOS
dc.identifier.doi10.1093/imanum/draa012
dc.identifier.eissn1464-3642
dc.identifier.issn0272-4979
dc.identifier.urihttps://doi.org/10.1093/imanum/draa012
dc.identifier.urihttps://repositorio.uc.cl/handle/11534/76723
dc.identifier.wosidWOS:000651815700008
dc.information.autorucFacultad de Matemáticas; Führer , Thomas; S/I; 250324
dc.issue.numero2
dc.language.isoen
dc.nota.accesocontenido parcial
dc.pagina.final1055
dc.pagina.inicio1031
dc.publisherOXFORD UNIV PRESS
dc.revistaIMA JOURNAL OF NUMERICAL ANALYSIS
dc.rightsacceso restringido
dc.subjectbi-Laplacian
dc.subjectbiharmonic operator
dc.subjecttrace operator
dc.subjectfourth-order elliptic PDE
dc.subjectultraweak formulation
dc.subjectdiscontinuous Petrov-Galerkin method
dc.subjectoptimal test functions
dc.subjectROBUST DPG METHOD
dc.subjectEQUATIONS
dc.subjectDOMAINS
dc.titleTrace operators of the bi-Laplacian and applications
dc.typeartículo
dc.volumen41
sipa.codpersvinculados250324
sipa.indexWOS
sipa.trazabilidadCarga SIPA;09-01-2024
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