A Continuous $hp-$Mesh Model for Discontinuous Petrov-Galerkin Finite Element Schemes with Optimal Test Functions
We present an anisotropic $hp-$mesh adaptation strategy using a continuous mesh model for discontinuous Petrov-Galerkin (DPG) finite element schemes with optimal test functions, extending our previous work on $h-$adaptation. The proposed strategy utilizes the inbuilt residual-based error estimator o...
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| creator | Chakraborty, Ankit May, Georg |
| description | We present an anisotropic $hp-$mesh adaptation strategy using a continuous
mesh model for discontinuous Petrov-Galerkin (DPG) finite element schemes with
optimal test functions, extending our previous work on $h-$adaptation. The
proposed strategy utilizes the inbuilt residual-based error estimator of the
DPG discretization to compute both the polynomial distribution and the
anisotropy of the mesh elements. In order to predict the optimal order of
approximation, we solve local problems on element patches, thus making these
computations highly parallelizable. The continuous mesh model is formulated
either with respect to the error in the solution, measured in a suitable norm,
or with respect to certain admissible target functionals. We demonstrate the
performance of the proposed strategy using several numerical examples on
triangular grids.
Keywords: Discontinuous Petrov-Galerkin, Continuous mesh models, $hp-$
adaptations, Anisotropy |
| doi_str_mv | 10.48550/arxiv.2211.11156 |
| format | Article |
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mesh model for discontinuous Petrov-Galerkin (DPG) finite element schemes with
optimal test functions, extending our previous work on $h-$adaptation. The
proposed strategy utilizes the inbuilt residual-based error estimator of the
DPG discretization to compute both the polynomial distribution and the
anisotropy of the mesh elements. In order to predict the optimal order of
approximation, we solve local problems on element patches, thus making these
computations highly parallelizable. The continuous mesh model is formulated
either with respect to the error in the solution, measured in a suitable norm,
or with respect to certain admissible target functionals. We demonstrate the
performance of the proposed strategy using several numerical examples on
triangular grids.
Keywords: Discontinuous Petrov-Galerkin, Continuous mesh models, $hp-$
adaptations, Anisotropy</description><identifier>DOI: 10.48550/arxiv.2211.11156</identifier><language>eng</language><subject>Computer Science - Computational Engineering, Finance, and Science</subject><creationdate>2022-11</creationdate><rights>http://arxiv.org/licenses/nonexclusive-distrib/1.0</rights><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>228,230,780,885</link.rule.ids><linktorsrc>$$Uhttps://arxiv.org/abs/2211.11156$$EView_record_in_Cornell_University$$FView_record_in_$$GCornell_University$$Hfree_for_read</linktorsrc><backlink>$$Uhttps://doi.org/10.48550/arXiv.2211.11156$$DView paper in arXiv$$Hfree_for_read</backlink></links><search><creatorcontrib>Chakraborty, Ankit</creatorcontrib><creatorcontrib>May, Georg</creatorcontrib><title>A Continuous $hp-$Mesh Model for Discontinuous Petrov-Galerkin Finite Element Schemes with Optimal Test Functions</title><description>We present an anisotropic $hp-$mesh adaptation strategy using a continuous
mesh model for discontinuous Petrov-Galerkin (DPG) finite element schemes with
optimal test functions, extending our previous work on $h-$adaptation. The
proposed strategy utilizes the inbuilt residual-based error estimator of the
DPG discretization to compute both the polynomial distribution and the
anisotropy of the mesh elements. In order to predict the optimal order of
approximation, we solve local problems on element patches, thus making these
computations highly parallelizable. The continuous mesh model is formulated
either with respect to the error in the solution, measured in a suitable norm,
or with respect to certain admissible target functionals. We demonstrate the
performance of the proposed strategy using several numerical examples on
triangular grids.
Keywords: Discontinuous Petrov-Galerkin, Continuous mesh models, $hp-$
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mesh model for discontinuous Petrov-Galerkin (DPG) finite element schemes with
optimal test functions, extending our previous work on $h-$adaptation. The
proposed strategy utilizes the inbuilt residual-based error estimator of the
DPG discretization to compute both the polynomial distribution and the
anisotropy of the mesh elements. In order to predict the optimal order of
approximation, we solve local problems on element patches, thus making these
computations highly parallelizable. The continuous mesh model is formulated
either with respect to the error in the solution, measured in a suitable norm,
or with respect to certain admissible target functionals. We demonstrate the
performance of the proposed strategy using several numerical examples on
triangular grids.
Keywords: Discontinuous Petrov-Galerkin, Continuous mesh models, $hp-$
adaptations, Anisotropy</abstract><doi>10.48550/arxiv.2211.11156</doi><oa>free_for_read</oa></addata></record> |
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| subjects | Computer Science - Computational Engineering, Finance, and Science |
| title | A Continuous $hp-$Mesh Model for Discontinuous Petrov-Galerkin Finite Element Schemes with Optimal Test Functions |
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