A MODIFIED WEAK GALERKIN FINITE ELEMENT METHOD FOR SOBOLEV EQUATION
For Sobolev equation, we present a new numerical scheme based on a modified weak Galerkin finite element method, in which differential operators are approximated by weak forms through the usual integration by parts. In particular, the numerical method allows the use of discontinuous finite element f...
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| Published in | Journal of computational mathematics Vol. 33; no. 3; pp. 307 - 322 |
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| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
Chinese Academy of Mathematices and System Sciences (AMSS) Chinese Academy of Sciences
01.05.2015
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| Subjects | |
| Online Access | Get full text |
| ISSN | 0254-9409 1991-7139 |
| DOI | 10.4208/jcm.1502-m4509 |
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| Abstract | For Sobolev equation, we present a new numerical scheme based on a modified weak Galerkin finite element method, in which differential operators are approximated by weak forms through the usual integration by parts. In particular, the numerical method allows the use of discontinuous finite element functions and arbitrary shape of element. Optimal order error estimates in discrete H^1 and L^2 norms are established for the corresponding modified weak Galerkin finite element solutions. Finally, some numerical results are given to verify theoretical results. |
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| AbstractList | For Sobolev equation, we present a new numerical scheme based on a modified weak Galerkin finite element method, in which differential operators are approximated by weak forms through the usual integration by parts. In particular, the numerical method allows the use of discontinuous finite element functions and arbitrary shape of element. Optimal order error estimates in discrete H¹ and L² norms are established for the corresponding modified weak Galerkin finite element solutions. Finally, some numerical results are given to verify theoretical results. For Sobolev equation, we present a new numerical scheme based on a modified weak Galerkin finite element method, in which differential operators are approximated by weak forms through the usual integration by parts. In particular, the numerical method allows the use of discontinuous finite element functions and arbitrary shape of element. Optimal order error estimates in discrete H^1 and L^2 norms are established for the corresponding modified weak Galerkin finite element solutions. Finally, some numerical results are given to verify theoretical results. |
| Author | Fuzheng Gao Xiaoshen Wang |
| AuthorAffiliation | School of Mathematics, Shandong University, Jinan, Shandong 250100, China School of Materials Science and Engineering, Shandong University, Jinan, Shandong, China Department of Mathematics, University of Arkansas at Little Rock, 2801 S. University Avenue, Little Rock, AR 72204, USA. |
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| CitedBy_id | crossref_primary_10_1016_j_camwa_2022_09_018 crossref_primary_10_1108_HFF_09_2021_0598 crossref_primary_10_1016_j_cam_2022_114979 crossref_primary_10_1016_j_camwa_2022_04_017 crossref_primary_10_1016_j_camwa_2025_01_013 crossref_primary_10_3934_dcdss_2024110 crossref_primary_10_1016_j_cam_2016_11_047 crossref_primary_10_1016_j_padiff_2020_100016 crossref_primary_10_1016_j_cnsns_2023_107440 crossref_primary_10_1016_j_apnum_2022_03_006 crossref_primary_10_1007_s10915_022_01997_3 crossref_primary_10_1002_mma_8579 crossref_primary_10_1016_j_aml_2023_108806 crossref_primary_10_1016_j_apnum_2020_08_010 crossref_primary_10_1002_num_22960 crossref_primary_10_1007_s13370_018_0626_9 crossref_primary_10_1016_j_apnum_2021_05_018 crossref_primary_10_1016_j_camwa_2018_09_058 crossref_primary_10_1515_jnma_2021_0012 |
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| Notes | 11-2126/O1 Galerkin FEMs, Sobolev equation, Discrete weak gradient, Modified weak Galerkin, Error estimate For Sobolev equation, we present a new numerical scheme based on a modified weak Galerkin finite element method, in which differential operators are approximated by weak forms through the usual integration by parts. In particular, the numerical method allows the use of discontinuous finite element functions and arbitrary shape of element. Optimal order error estimates in discrete H^1 and L^2 norms are established for the corresponding modified weak Galerkin finite element solutions. Finally, some numerical results are given to verify theoretical results. |
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| PublicationTitle | Journal of computational mathematics |
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| Snippet | For Sobolev equation, we present a new numerical scheme based on a modified weak Galerkin finite element method, in which differential operators are... |
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| StartPage | 307 |
| SubjectTerms | Galerkin有限元法 Sobolev方程 任意形状 微分算子 数值方法 最优误差估计 索伯列夫方程 间断有限元 |
| Title | A MODIFIED WEAK GALERKIN FINITE ELEMENT METHOD FOR SOBOLEV EQUATION |
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