A Priori Error Analysis for the hp-Version of the Discontinuous Galerkin Finite Element Method for the Biharmonic Equation
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| 024 | 7 | 0 | |a 10.2478/cmam-2003-0037 |2 doi |
| 035 | |a (NATIONALLICENCE)gruyter-10.2478/cmam-2003-0037 | ||
| 245 | 0 | 2 | |a A Priori Error Analysis for the hp-Version of the Discontinuous Galerkin Finite Element Method for the Biharmonic Equation |h [Elektronische Daten] |
| 520 | 3 | |a 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. | |
| 540 | |a This article is distributed under the terms of the Creative Commons Attribution Non-Commercial License, which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited. | ||
| 690 | 7 | |a discontinuous Galerkin methods |2 nationallicence | |
| 690 | 7 | |a biharmonic equation |2 nationallicence | |
| 690 | 7 | |a thin plate theory |2 nationallicence | |
| 700 | 1 | |a Mozolevski |D Igor |u Federal University of Santa Catarina, Mathematical Department Trindade, Florian´opolis, SC, 88040-900, Brazil. | |
| 700 | 1 | |a Süli |D Endre |u Oxford University Computing Laboratory, Wolfson Building, Parks Road, Oxford OX1 3QD, UK. | |
| 773 | 0 | |t Computational Methods in Applied Mathematics |d De Gruyter |g 3/4(2003), 596-607 |x 1609-4840 |q 3:4<596 |1 2003 |2 3 |o cmam | |
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| 908 | |D 1 |a research article |2 jats | ||
| 950 | |B NATIONALLICENCE |P 856 |E 40 |u https://doi.org/10.2478/cmam-2003-0037 |q text/html |z Onlinezugriff via DOI | ||
| 950 | |B NATIONALLICENCE |P 700 |E 1- |a Mozolevski |D Igor |u Federal University of Santa Catarina, Mathematical Department Trindade, Florian´opolis, SC, 88040-900, Brazil | ||
| 950 | |B NATIONALLICENCE |P 700 |E 1- |a Süli |D Endre |u Oxford University Computing Laboratory, Wolfson Building, Parks Road, Oxford OX1 3QD, UK | ||
| 950 | |B NATIONALLICENCE |P 773 |E 0- |t Computational Methods in Applied Mathematics |d De Gruyter |g 3/4(2003), 596-607 |x 1609-4840 |q 3:4<596 |1 2003 |2 3 |o cmam | ||
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