Numerical Solution of Burgers’ Equation Based on Mixed Finite Volume Element Methods
In this article, mixed finite volume element (MFVE) methods are proposed for solving the numerical solution of Burgers’ equation. By introducing a transfer operator, semidiscrete and fully discrete MFVE schemes are constructed. The existence, uniqueness, and stability analyses for semidiscrete and f...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2020-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2020/6321209 |
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| _version_ | 1832547728265052160 |
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| author | Jie Zhao Hong Li Zhichao Fang Xue Bai |
| author_facet | Jie Zhao Hong Li Zhichao Fang Xue Bai |
| author_sort | Jie Zhao |
| collection | DOAJ |
| description | In this article, mixed finite volume element (MFVE) methods are proposed for solving the numerical solution of Burgers’ equation. By introducing a transfer operator, semidiscrete and fully discrete MFVE schemes are constructed. The existence, uniqueness, and stability analyses for semidiscrete and fully discrete MFVE schemes are given in detail. The optimal a priori error estimates for the unknown and auxiliary variables in the L2Ω norm are derived by using the stability results. Finally, numerical results are given to verify the feasibility and effectiveness. |
| format | Article |
| id | doaj-art-af8ca19fb03d41ac9e6a733e7f9a304b |
| institution | Kabale University |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2020-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-af8ca19fb03d41ac9e6a733e7f9a304b2025-02-03T06:43:41ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2020-01-01202010.1155/2020/63212096321209Numerical Solution of Burgers’ Equation Based on Mixed Finite Volume Element MethodsJie Zhao0Hong Li1Zhichao Fang2Xue Bai3School 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, ChinaSchool of Mathematical Sciences, Inner Mongolia University, Hohhot 010021, ChinaIn this article, mixed finite volume element (MFVE) methods are proposed for solving the numerical solution of Burgers’ equation. By introducing a transfer operator, semidiscrete and fully discrete MFVE schemes are constructed. The existence, uniqueness, and stability analyses for semidiscrete and fully discrete MFVE schemes are given in detail. The optimal a priori error estimates for the unknown and auxiliary variables in the L2Ω norm are derived by using the stability results. Finally, numerical results are given to verify the feasibility and effectiveness.http://dx.doi.org/10.1155/2020/6321209 |
| spellingShingle | Jie Zhao Hong Li Zhichao Fang Xue Bai Numerical Solution of Burgers’ Equation Based on Mixed Finite Volume Element Methods Discrete Dynamics in Nature and Society |
| title | Numerical Solution of Burgers’ Equation Based on Mixed Finite Volume Element Methods |
| title_full | Numerical Solution of Burgers’ Equation Based on Mixed Finite Volume Element Methods |
| title_fullStr | Numerical Solution of Burgers’ Equation Based on Mixed Finite Volume Element Methods |
| title_full_unstemmed | Numerical Solution of Burgers’ Equation Based on Mixed Finite Volume Element Methods |
| title_short | Numerical Solution of Burgers’ Equation Based on Mixed Finite Volume Element Methods |
| title_sort | numerical solution of burgers equation based on mixed finite volume element methods |
| url | http://dx.doi.org/10.1155/2020/6321209 |
| work_keys_str_mv | AT jiezhao numericalsolutionofburgersequationbasedonmixedfinitevolumeelementmethods AT hongli numericalsolutionofburgersequationbasedonmixedfinitevolumeelementmethods AT zhichaofang numericalsolutionofburgersequationbasedonmixedfinitevolumeelementmethods AT xuebai numericalsolutionofburgersequationbasedonmixedfinitevolumeelementmethods |