The Local Discontinuous Galerkin Method with Generalized Alternating Flux Applied to the Second-Order Wave Equations
In this paper, we propose the local discontinuous Galerkin method based on the generalized alternating numerical flux for solving the one-dimensional second-order wave equation with the periodic boundary conditions. Introducing two auxiliary variables, the second-order equation is rewritten into the...
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| Format: | Article |
| Language: | English |
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Wiley
2020-01-01
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| Series: | Complexity |
| Online Access: | http://dx.doi.org/10.1155/2020/8464153 |
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| _version_ | 1832550978288615424 |
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| author | Rongpei Zhang Jia Liu Shaohua Jiang Di Wang |
| author_facet | Rongpei Zhang Jia Liu Shaohua Jiang Di Wang |
| author_sort | Rongpei Zhang |
| collection | DOAJ |
| description | In this paper, we propose the local discontinuous Galerkin method based on the generalized alternating numerical flux for solving the one-dimensional second-order wave equation with the periodic boundary conditions. Introducing two auxiliary variables, the second-order equation is rewritten into the first-order equation systems. We prove the stability and energy conservation of this method. By virtue of the generalized Gauss–Radau projection, we can obtain the optimal convergence order in L2-norm of Ohk+1 with polynomial of degree k and grid size h. Numerical experiments are given to verify the theoretical results. |
| format | Article |
| id | doaj-art-66f59e8637a743238a3c864e4d69abfc |
| institution | Kabale University |
| issn | 1076-2787 1099-0526 |
| language | English |
| publishDate | 2020-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Complexity |
| spelling | doaj-art-66f59e8637a743238a3c864e4d69abfc2025-02-03T06:05:12ZengWileyComplexity1076-27871099-05262020-01-01202010.1155/2020/84641538464153The Local Discontinuous Galerkin Method with Generalized Alternating Flux Applied to the Second-Order Wave EquationsRongpei Zhang0Jia Liu1Shaohua Jiang2Di Wang3School of Mathematics and Systematic Sciences, Shenyang Normal University, Shenyang 110034, ChinaDepartment of Foreign Language, Shenyang Normal University, Shenyang 110034, ChinaSchool of Art and Design, Shenyang Normal University, Shenyang 110034, ChinaSchool of Mathematics and Systematic Sciences, Shenyang Normal University, Shenyang 110034, ChinaIn this paper, we propose the local discontinuous Galerkin method based on the generalized alternating numerical flux for solving the one-dimensional second-order wave equation with the periodic boundary conditions. Introducing two auxiliary variables, the second-order equation is rewritten into the first-order equation systems. We prove the stability and energy conservation of this method. By virtue of the generalized Gauss–Radau projection, we can obtain the optimal convergence order in L2-norm of Ohk+1 with polynomial of degree k and grid size h. Numerical experiments are given to verify the theoretical results.http://dx.doi.org/10.1155/2020/8464153 |
| spellingShingle | Rongpei Zhang Jia Liu Shaohua Jiang Di Wang The Local Discontinuous Galerkin Method with Generalized Alternating Flux Applied to the Second-Order Wave Equations Complexity |
| title | The Local Discontinuous Galerkin Method with Generalized Alternating Flux Applied to the Second-Order Wave Equations |
| title_full | The Local Discontinuous Galerkin Method with Generalized Alternating Flux Applied to the Second-Order Wave Equations |
| title_fullStr | The Local Discontinuous Galerkin Method with Generalized Alternating Flux Applied to the Second-Order Wave Equations |
| title_full_unstemmed | The Local Discontinuous Galerkin Method with Generalized Alternating Flux Applied to the Second-Order Wave Equations |
| title_short | The Local Discontinuous Galerkin Method with Generalized Alternating Flux Applied to the Second-Order Wave Equations |
| title_sort | local discontinuous galerkin method with generalized alternating flux applied to the second order wave equations |
| url | http://dx.doi.org/10.1155/2020/8464153 |
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