A Priori Error Analysis for the hp-Version of the Discontinuous Galerkin Finite Element Method for the Biharmonic Equation
Abstract: We consider the hp-version of the discontinuous Galerkin finite element approximation of boundary value problems for the biharmonic equation. Our main concern is the a priori error analysis of the method, based on a nonsymmetric bilinear form with interior discontinuity penalization terms. We establish an a priori error bound for the method which is of optimal order with respect to the mesh size h, and nearly optimal with respect to the degree p of the polynomial approximation. For analytic solutions, the method exhibits an exponential rate of convergence under p- refinement. These results are shown in the DG-norm for a general shape regular family of partitions consisting of d-dimensional parallelepipeds. The theoretical results are confirmed by numerical experiments. The method has also been tested on several practical problems of thin-plate-bending theory and has been shown to be competitive in accuracy with existing algorithms.
- Standort
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Deutsche Nationalbibliothek Frankfurt am Main
- Umfang
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Online-Ressource
- Sprache
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Englisch
- Erschienen in
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A Priori Error Analysis for the hp-Version of the Discontinuous Galerkin Finite Element Method for the Biharmonic Equation ; volume:3 ; number:4 ; year:2003 ; pages:596-607
Computational methods in applied mathematics ; 3, Heft 4 (2003), 596-607
- Urheber
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Mozolevski, Igor
Süli, Endre
- DOI
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10.2478/cmam-2003-0037
- URN
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urn:nbn:de:101:1-2410261614339.720962380632
- Rechteinformation
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Open Access; Der Zugriff auf das Objekt ist unbeschränkt möglich.
- Letzte Aktualisierung
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15.08.2025, 07:21 MESZ
Datenpartner
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Beteiligte
- Mozolevski, Igor
- Süli, Endre
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