<div class="csl-bib-body">
<div class="csl-entry">Bringmann, P., Carstensen, C., & Streitberger, J. (2023). Local parameter selection in the C<sup>0</sup> interior penalty method for the biharmonic equation. <i>Journal of Numerical Mathematics</i>. https://doi.org/10.1515/jnma-2023-0028</div>
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dc.identifier.issn
1570-2820
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dc.identifier.uri
http://hdl.handle.net/20.500.12708/188249
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dc.description.abstract
The symmetric C0 interior penalty method is one of the most popular discontinuous Galerkin methods for the biharmonic equation. This paper introduces an automatic local selection of the involved stability parameter in terms of the geometry of the underlying triangulation for arbitrary polynomial degrees. The proposed choice ensures a stable discretization with guaranteed discrete ellipticity constant. Numerical evidence for uniform and adaptive mesh-refinement and various polynomial degrees supports the reliability and efficiency of the local parameter selection and recommends this in practice. The approach is documented in 2D for triangles, but the methodology behind can be generalized to higher dimensions, to non-uniform polynomial degrees, and to rectangular discretizations. An appendix presents the realization of our proposed parameter selection in various established finite element software packages.
en
dc.language.iso
en
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dc.publisher
WALTER DE GRUYTER GMBH
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dc.relation.ispartof
Journal of Numerical Mathematics
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dc.subject
C0 interior penalty method
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dc.subject
Discontinuous Galerkin method
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dc.subject
biharmonic equation
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dc.subject
implementation
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dc.subject
local parameter selection
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dc.subject
penalty parameter
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dc.title
Local parameter selection in the C⁰ interior penalty method for the biharmonic equation