A Time Discontinuous Galerkin Finite Element Method for Quasi-Linear Sobolev Equations
We present a time discontinuous Galerkin finite element scheme for quasi-linear Sobolev equations. The approximate solution is sought as a piecewise polynomial of degree in time variable at most q-1 with coefficients in finite element space. This piecewise polynomial is not necessarily continuous at...
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| Format: | Article |
| Language: | English |
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Wiley
2015-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2015/985214 |
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| _version_ | 1832550493338992640 |
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| author | Hong Yu Tongjun Sun |
| author_facet | Hong Yu Tongjun Sun |
| author_sort | Hong Yu |
| collection | DOAJ |
| description | We present a time discontinuous Galerkin finite element scheme for quasi-linear Sobolev equations. The approximate solution is sought as a piecewise polynomial of degree in time variable at most q-1 with coefficients in finite element space. This piecewise polynomial is not necessarily continuous at the nodes of the partition for the time interval. The existence and uniqueness of the approximate solution are proved by use of Brouwer’s fixed point theorem. An optimal L∞(0,T;H1(Ω))-norm error estimate is derived. Just because of a damping term uxxt included in quasi-linear Sobolev equations, which is the distinct character different from parabolic equation, more attentions are paid to this term in the study. This is the significance of this paper. |
| format | Article |
| id | doaj-art-73141712fb9440458cd3aa34f7ca9e51 |
| institution | Kabale University |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2015-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-73141712fb9440458cd3aa34f7ca9e512025-02-03T06:06:36ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2015-01-01201510.1155/2015/985214985214A Time Discontinuous Galerkin Finite Element Method for Quasi-Linear Sobolev EquationsHong Yu0Tongjun Sun1Basic Subject Department, Shandong Women’s University, Jinan, Shandong 250300, ChinaSchool of Mathematics, Shandong University, Jinan, Shandong 250100, ChinaWe present a time discontinuous Galerkin finite element scheme for quasi-linear Sobolev equations. The approximate solution is sought as a piecewise polynomial of degree in time variable at most q-1 with coefficients in finite element space. This piecewise polynomial is not necessarily continuous at the nodes of the partition for the time interval. The existence and uniqueness of the approximate solution are proved by use of Brouwer’s fixed point theorem. An optimal L∞(0,T;H1(Ω))-norm error estimate is derived. Just because of a damping term uxxt included in quasi-linear Sobolev equations, which is the distinct character different from parabolic equation, more attentions are paid to this term in the study. This is the significance of this paper.http://dx.doi.org/10.1155/2015/985214 |
| spellingShingle | Hong Yu Tongjun Sun A Time Discontinuous Galerkin Finite Element Method for Quasi-Linear Sobolev Equations Discrete Dynamics in Nature and Society |
| title | A Time Discontinuous Galerkin Finite Element Method for Quasi-Linear Sobolev Equations |
| title_full | A Time Discontinuous Galerkin Finite Element Method for Quasi-Linear Sobolev Equations |
| title_fullStr | A Time Discontinuous Galerkin Finite Element Method for Quasi-Linear Sobolev Equations |
| title_full_unstemmed | A Time Discontinuous Galerkin Finite Element Method for Quasi-Linear Sobolev Equations |
| title_short | A Time Discontinuous Galerkin Finite Element Method for Quasi-Linear Sobolev Equations |
| title_sort | time discontinuous galerkin finite element method for quasi linear sobolev equations |
| url | http://dx.doi.org/10.1155/2015/985214 |
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