A posteriori error estimate for Reissner-Mindlin plates: verification of implementations and numerical testing
Work is devoted to analysis of a posteriori error estimate for accuracy control of approximate solutions for problems of Reissner-Mindlin plates bending. The estimate is constructed with the functional approach, which is based on rigorous mathematical grounds, in particular, on methods of functional...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Peter the Great St.Petersburg Polytechnic University
2019-03-01
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| Series: | St. Petersburg Polytechnical University Journal: Physics and Mathematics |
| Subjects: | |
| Online Access: | https://physmath.spbstu.ru/article/2019.43.11/ |
| _version_ | 1819136441702154240 |
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| author | Kiselev Kirill Frolov Maxim Chistiakova Olga |
| author_facet | Kiselev Kirill Frolov Maxim Chistiakova Olga |
| author_sort | Kiselev Kirill |
| collection | DOAJ |
| description | Work is devoted to analysis of a posteriori error estimate for accuracy control of approximate solutions for problems of Reissner-Mindlin plates bending. The estimate is constructed with the functional approach, which is based on rigorous mathematical grounds, in particular, on methods of functional analysis. It is valid for all conforming approximations of exact solutions, and therefore, it is reliable. The estimate is guaranteed in practical implementations due to robustness of the respective inequality. The above-mentioned properties of the method of error control are very desirable for engineering analysis, where some details might be hidden. Paper investigates two independent implementations of the estimate. Using specially constructed numerical tests, correctness of both implementation algorithms and similarity of the obtained results for all examples are shown. For a wide range of values of plate thicknesses, an overestimation of the true error remains acceptable. |
| first_indexed | 2024-12-22T10:35:02Z |
| format | Article |
| id | doaj.art-54a3a3db31f94ffdada9a4f2ae6cf065 |
| institution | Directory Open Access Journal |
| issn | 2405-7223 |
| language | English |
| last_indexed | 2024-12-22T10:35:02Z |
| publishDate | 2019-03-01 |
| publisher | Peter the Great St.Petersburg Polytechnic University |
| record_format | Article |
| series | St. Petersburg Polytechnical University Journal: Physics and Mathematics |
| spelling | doaj.art-54a3a3db31f94ffdada9a4f2ae6cf0652022-12-21T18:29:13ZengPeter the Great St.Petersburg Polytechnic UniversitySt. Petersburg Polytechnical University Journal: Physics and Mathematics2405-72232019-03-0112110.18721/JPM.1211120714726A posteriori error estimate for Reissner-Mindlin plates: verification of implementations and numerical testingKiselev Kirill0Frolov Maxim1Chistiakova Olga2Peter the Great St. Petersburg Polytechnic UniversityPeter the Great St. Petersburg Polytechnic UniversityPeter the Great St. Petersburg Polytechnic UniversityWork is devoted to analysis of a posteriori error estimate for accuracy control of approximate solutions for problems of Reissner-Mindlin plates bending. The estimate is constructed with the functional approach, which is based on rigorous mathematical grounds, in particular, on methods of functional analysis. It is valid for all conforming approximations of exact solutions, and therefore, it is reliable. The estimate is guaranteed in practical implementations due to robustness of the respective inequality. The above-mentioned properties of the method of error control are very desirable for engineering analysis, where some details might be hidden. Paper investigates two independent implementations of the estimate. Using specially constructed numerical tests, correctness of both implementation algorithms and similarity of the obtained results for all examples are shown. For a wide range of values of plate thicknesses, an overestimation of the true error remains acceptable.https://physmath.spbstu.ru/article/2019.43.11/a posteriori error estimatefinite element methodreissner – mindlin plate |
| spellingShingle | Kiselev Kirill Frolov Maxim Chistiakova Olga A posteriori error estimate for Reissner-Mindlin plates: verification of implementations and numerical testing St. Petersburg Polytechnical University Journal: Physics and Mathematics a posteriori error estimate finite element method reissner – mindlin plate |
| title | A posteriori error estimate for Reissner-Mindlin plates: verification of implementations and numerical testing |
| title_full | A posteriori error estimate for Reissner-Mindlin plates: verification of implementations and numerical testing |
| title_fullStr | A posteriori error estimate for Reissner-Mindlin plates: verification of implementations and numerical testing |
| title_full_unstemmed | A posteriori error estimate for Reissner-Mindlin plates: verification of implementations and numerical testing |
| title_short | A posteriori error estimate for Reissner-Mindlin plates: verification of implementations and numerical testing |
| title_sort | posteriori error estimate for reissner mindlin plates verification of implementations and numerical testing |
| topic | a posteriori error estimate finite element method reissner – mindlin plate |
| url | https://physmath.spbstu.ru/article/2019.43.11/ |
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