A posteriori error estimates for elliptic problems in two and three space dimensions:
Abstract: "Let u [element of] H be the exact solution of a given self-adjoint elliptic boundary value problem, which is approximated by some u [element of] S, S being a suitable finite element space. Efficient and reliable a posteriori estimates of the error [parallel] u - u, measuring the (loc...
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| Main Authors: | , , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin
Konrad-Zuse-Zentrum für Informationstechnik
1993
|
| Series: | Konrad-Zuse-Zentrum für Informationstechnik <Berlin>: Preprint SC
1993,29 |
| Subjects: | |
| Summary: | Abstract: "Let u [element of] H be the exact solution of a given self-adjoint elliptic boundary value problem, which is approximated by some u [element of] S, S being a suitable finite element space. Efficient and reliable a posteriori estimates of the error [parallel] u - u, measuring the (local) quality of u, play a crucial role in termination criteria and in the adaptive refinement of the underlying mesh. A well-known class of error estimates can be derived systematically by localizing the discretized defect problem using domain decomposition techniques. In the present paper, we provide a guideline for the theoretical analysis of such error estimates. We further clarify the relation to other concepts. Our analysis leads to new error estimates, which are specially suited to three space dimensions The theoretical results are illustrated by numerical computations. |
| Physical Description: | 24 S. |
Staff View
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| 100 | 1 | |a Bornemann, Folkmar |d 1967- |e Verfasser |0 (DE-588)120096269 |4 aut | |
| 245 | 1 | 0 | |a A posteriori error estimates for elliptic problems in two and three space dimensions |c Folkmar Bornemann ; Bodo Erdmann, Ralf Kornhuber |
| 264 | 1 | |a Berlin |b Konrad-Zuse-Zentrum für Informationstechnik |c 1993 | |
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| 490 | 1 | |a Konrad-Zuse-Zentrum für Informationstechnik <Berlin>: Preprint SC |v 1993,29 | |
| 520 | 3 | |a Abstract: "Let u [element of] H be the exact solution of a given self-adjoint elliptic boundary value problem, which is approximated by some u [element of] S, S being a suitable finite element space. Efficient and reliable a posteriori estimates of the error [parallel] u - u, measuring the (local) quality of u, play a crucial role in termination criteria and in the adaptive refinement of the underlying mesh. A well-known class of error estimates can be derived systematically by localizing the discretized defect problem using domain decomposition techniques. In the present paper, we provide a guideline for the theoretical analysis of such error estimates. We further clarify the relation to other concepts. Our analysis leads to new error estimates, which are specially suited to three space dimensions | |
| 520 | 3 | |a The theoretical results are illustrated by numerical computations. | |
| 650 | 4 | |a Boundary value problems | |
| 700 | 1 | |a Erdmann, Bodo |e Verfasser |4 aut | |
| 700 | 1 | |a Kornhuber, Ralf |e Verfasser |4 aut | |
| 830 | 0 | |a Konrad-Zuse-Zentrum für Informationstechnik <Berlin>: Preprint SC |v 1993,29 |w (DE-604)BV004801715 |9 1993,29 | |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-006184463 | ||
Record in the Search Index
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| author | Bornemann, Folkmar 1967- Erdmann, Bodo Kornhuber, Ralf |
| author_GND | (DE-588)120096269 |
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| bvnumber | BV009294106 |
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| id | DE-604.BV009294106 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T17:34:29Z |
| institution | BVB |
| language | English |
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| physical | 24 S. |
| publishDate | 1993 |
| publishDateSearch | 1993 |
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| publisher | Konrad-Zuse-Zentrum für Informationstechnik |
| record_format | marc |
| series | Konrad-Zuse-Zentrum für Informationstechnik <Berlin>: Preprint SC |
| series2 | Konrad-Zuse-Zentrum für Informationstechnik <Berlin>: Preprint SC |
| spelling | Bornemann, Folkmar 1967- Verfasser (DE-588)120096269 aut A posteriori error estimates for elliptic problems in two and three space dimensions Folkmar Bornemann ; Bodo Erdmann, Ralf Kornhuber Berlin Konrad-Zuse-Zentrum für Informationstechnik 1993 24 S. txt rdacontent n rdamedia nc rdacarrier Konrad-Zuse-Zentrum für Informationstechnik <Berlin>: Preprint SC 1993,29 Abstract: "Let u [element of] H be the exact solution of a given self-adjoint elliptic boundary value problem, which is approximated by some u [element of] S, S being a suitable finite element space. Efficient and reliable a posteriori estimates of the error [parallel] u - u, measuring the (local) quality of u, play a crucial role in termination criteria and in the adaptive refinement of the underlying mesh. A well-known class of error estimates can be derived systematically by localizing the discretized defect problem using domain decomposition techniques. In the present paper, we provide a guideline for the theoretical analysis of such error estimates. We further clarify the relation to other concepts. Our analysis leads to new error estimates, which are specially suited to three space dimensions The theoretical results are illustrated by numerical computations. Boundary value problems Erdmann, Bodo Verfasser aut Kornhuber, Ralf Verfasser aut Konrad-Zuse-Zentrum für Informationstechnik <Berlin>: Preprint SC 1993,29 (DE-604)BV004801715 1993,29 |
| spellingShingle | Bornemann, Folkmar 1967- Erdmann, Bodo Kornhuber, Ralf A posteriori error estimates for elliptic problems in two and three space dimensions Konrad-Zuse-Zentrum für Informationstechnik <Berlin>: Preprint SC Boundary value problems |
| title | A posteriori error estimates for elliptic problems in two and three space dimensions |
| title_auth | A posteriori error estimates for elliptic problems in two and three space dimensions |
| title_exact_search | A posteriori error estimates for elliptic problems in two and three space dimensions |
| title_full | A posteriori error estimates for elliptic problems in two and three space dimensions Folkmar Bornemann ; Bodo Erdmann, Ralf Kornhuber |
| title_fullStr | A posteriori error estimates for elliptic problems in two and three space dimensions Folkmar Bornemann ; Bodo Erdmann, Ralf Kornhuber |
| title_full_unstemmed | A posteriori error estimates for elliptic problems in two and three space dimensions Folkmar Bornemann ; Bodo Erdmann, Ralf Kornhuber |
| title_short | A posteriori error estimates for elliptic problems in two and three space dimensions |
| title_sort | a posteriori error estimates for elliptic problems in two and three space dimensions |
| topic | Boundary value problems |
| topic_facet | Boundary value problems |
| volume_link | (DE-604)BV004801715 |
| work_keys_str_mv | AT bornemannfolkmar aposteriorierrorestimatesforellipticproblemsintwoandthreespacedimensions AT erdmannbodo aposteriorierrorestimatesforellipticproblemsintwoandthreespacedimensions AT kornhuberralf aposteriorierrorestimatesforellipticproblemsintwoandthreespacedimensions |