Unconditional superconvergence analysis of an energy-stable finite element scheme for nonlinear Benjamin–Bona–Mahony–Burgers equation
Abstract In this paper, an energy-stable Crank–Nicolson fully discrete finite element scheme is proposed for the Benjamin–Bona–Mahony–Burgers equation. Firstly, the stability of energy is proved, which leads to the boundedness of the finite element solution in H 1 $H^{1}$ -norm. Secondly, combining...
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
SpringerOpen
2022-09-01
|
| Series: | Boundary Value Problems |
| Subjects: | |
| Online Access: | https://doi.org/10.1186/s13661-022-01651-9 |
| _version_ | 1818024798270259200 |
|---|---|
| author | Lele Wang Xin Liao Huaijun Yang |
| author_facet | Lele Wang Xin Liao Huaijun Yang |
| author_sort | Lele Wang |
| collection | DOAJ |
| description | Abstract In this paper, an energy-stable Crank–Nicolson fully discrete finite element scheme is proposed for the Benjamin–Bona–Mahony–Burgers equation. Firstly, the stability of energy is proved, which leads to the boundedness of the finite element solution in H 1 $H^{1}$ -norm. Secondly, combining with the above boundedness and the special property of bilinear element, the unconditional superclose and superconvergence results are derived. Finally, numerical examples are provided to illustrate the validity and efficiency of our theoretical analysis and method. |
| first_indexed | 2024-12-10T04:05:56Z |
| format | Article |
| id | doaj.art-68f580c43d2c4165ad40050cfd3a9f62 |
| institution | Directory Open Access Journal |
| issn | 1687-2770 |
| language | English |
| last_indexed | 2024-12-10T04:05:56Z |
| publishDate | 2022-09-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Boundary Value Problems |
| spelling | doaj.art-68f580c43d2c4165ad40050cfd3a9f622022-12-22T02:02:51ZengSpringerOpenBoundary Value Problems1687-27702022-09-012022111310.1186/s13661-022-01651-9Unconditional superconvergence analysis of an energy-stable finite element scheme for nonlinear Benjamin–Bona–Mahony–Burgers equationLele Wang0Xin Liao1Huaijun Yang2School of Mathematics, Zhengzhou University of AeronauticsSchool of Mathematics, Zhengzhou University of AeronauticsSchool of Mathematics, Zhengzhou University of AeronauticsAbstract In this paper, an energy-stable Crank–Nicolson fully discrete finite element scheme is proposed for the Benjamin–Bona–Mahony–Burgers equation. Firstly, the stability of energy is proved, which leads to the boundedness of the finite element solution in H 1 $H^{1}$ -norm. Secondly, combining with the above boundedness and the special property of bilinear element, the unconditional superclose and superconvergence results are derived. Finally, numerical examples are provided to illustrate the validity and efficiency of our theoretical analysis and method.https://doi.org/10.1186/s13661-022-01651-9Benjamin–Bona–Mahony–Burgers equationEnergy-stable schemeUnconditional superconvergence analysis |
| spellingShingle | Lele Wang Xin Liao Huaijun Yang Unconditional superconvergence analysis of an energy-stable finite element scheme for nonlinear Benjamin–Bona–Mahony–Burgers equation Boundary Value Problems Benjamin–Bona–Mahony–Burgers equation Energy-stable scheme Unconditional superconvergence analysis |
| title | Unconditional superconvergence analysis of an energy-stable finite element scheme for nonlinear Benjamin–Bona–Mahony–Burgers equation |
| title_full | Unconditional superconvergence analysis of an energy-stable finite element scheme for nonlinear Benjamin–Bona–Mahony–Burgers equation |
| title_fullStr | Unconditional superconvergence analysis of an energy-stable finite element scheme for nonlinear Benjamin–Bona–Mahony–Burgers equation |
| title_full_unstemmed | Unconditional superconvergence analysis of an energy-stable finite element scheme for nonlinear Benjamin–Bona–Mahony–Burgers equation |
| title_short | Unconditional superconvergence analysis of an energy-stable finite element scheme for nonlinear Benjamin–Bona–Mahony–Burgers equation |
| title_sort | unconditional superconvergence analysis of an energy stable finite element scheme for nonlinear benjamin bona mahony burgers equation |
| topic | Benjamin–Bona–Mahony–Burgers equation Energy-stable scheme Unconditional superconvergence analysis |
| url | https://doi.org/10.1186/s13661-022-01651-9 |
| work_keys_str_mv | AT lelewang unconditionalsuperconvergenceanalysisofanenergystablefiniteelementschemefornonlinearbenjaminbonamahonyburgersequation AT xinliao unconditionalsuperconvergenceanalysisofanenergystablefiniteelementschemefornonlinearbenjaminbonamahonyburgersequation AT huaijunyang unconditionalsuperconvergenceanalysisofanenergystablefiniteelementschemefornonlinearbenjaminbonamahonyburgersequation |