A New Expanded Mixed Element Method for Convection-Dominated Sobolev Equation
We propose and analyze a new expanded mixed element method, whose gradient belongs to the simple square integrable space instead of the classical H(div; Ω) space of Chen’s expanded mixed element method. We study the new expanded mixed element method for convection-dominated Sobolev equation, prove t...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | The Scientific World Journal |
| Online Access: | http://dx.doi.org/10.1155/2014/297825 |
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| _version_ | 1832561069372997632 |
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| author | Jinfeng Wang Yang Liu Hong Li Zhichao Fang |
| author_facet | Jinfeng Wang Yang Liu Hong Li Zhichao Fang |
| author_sort | Jinfeng Wang |
| collection | DOAJ |
| description | We propose and analyze a new expanded mixed element method, whose gradient belongs to the simple square integrable space instead of the classical H(div; Ω) space of Chen’s expanded mixed element method. We study the new expanded mixed element method for convection-dominated Sobolev equation, prove the existence and uniqueness for finite element solution, and introduce a new expanded mixed projection. We derive the optimal a priori error estimates in L2-norm for the scalar unknown u and a priori error estimates in (L2)2-norm for its gradient λ and its flux σ. Moreover, we obtain the optimal a priori error estimates in H1-norm for the scalar unknown u. Finally, we obtained some numerical results to illustrate efficiency of the new method. |
| format | Article |
| id | doaj-art-e315332e67ff45b78e9bc0c5cfca31bc |
| institution | Kabale University |
| issn | 2356-6140 1537-744X |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | The Scientific World Journal |
| spelling | doaj-art-e315332e67ff45b78e9bc0c5cfca31bc2025-02-03T01:26:04ZengWileyThe Scientific World Journal2356-61401537-744X2014-01-01201410.1155/2014/297825297825A New Expanded Mixed Element Method for Convection-Dominated Sobolev EquationJinfeng Wang0Yang Liu1Hong Li2Zhichao Fang3School of Statistics and Mathematics, Inner Mongolia University of Finance and Economics, Hohhot 010070, ChinaSchool of Mathematical Sciences, Inner Mongolia University, Hohhot 010021, ChinaSchool of Mathematical Sciences, Inner Mongolia University, Hohhot 010021, ChinaSchool of Mathematical Sciences, Inner Mongolia University, Hohhot 010021, ChinaWe propose and analyze a new expanded mixed element method, whose gradient belongs to the simple square integrable space instead of the classical H(div; Ω) space of Chen’s expanded mixed element method. We study the new expanded mixed element method for convection-dominated Sobolev equation, prove the existence and uniqueness for finite element solution, and introduce a new expanded mixed projection. We derive the optimal a priori error estimates in L2-norm for the scalar unknown u and a priori error estimates in (L2)2-norm for its gradient λ and its flux σ. Moreover, we obtain the optimal a priori error estimates in H1-norm for the scalar unknown u. Finally, we obtained some numerical results to illustrate efficiency of the new method.http://dx.doi.org/10.1155/2014/297825 |
| spellingShingle | Jinfeng Wang Yang Liu Hong Li Zhichao Fang A New Expanded Mixed Element Method for Convection-Dominated Sobolev Equation The Scientific World Journal |
| title | A New Expanded Mixed Element Method for Convection-Dominated Sobolev Equation |
| title_full | A New Expanded Mixed Element Method for Convection-Dominated Sobolev Equation |
| title_fullStr | A New Expanded Mixed Element Method for Convection-Dominated Sobolev Equation |
| title_full_unstemmed | A New Expanded Mixed Element Method for Convection-Dominated Sobolev Equation |
| title_short | A New Expanded Mixed Element Method for Convection-Dominated Sobolev Equation |
| title_sort | new expanded mixed element method for convection dominated sobolev equation |
| url | http://dx.doi.org/10.1155/2014/297825 |
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