Error Estimates on Hybridizable Discontinuous Galerkin Methods for Parabolic Equations with Nonlinear Coefficients
HDG method has been widely used as an effective numerical technique to obtain physically relevant solutions for PDE. In a practical setting, PDE comes with nonlinear coefficients. Hence, it is inevitable to consider how to obtain an approximate solution for PDE with nonlinear coefficients. Research...
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| Format: | Article |
| Language: | English |
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Wiley
2017-01-01
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| Series: | Advances in Mathematical Physics |
| Online Access: | http://dx.doi.org/10.1155/2017/9736818 |
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| author | Minam Moon Hyung Kyu Jun Tay Suh |
| author_facet | Minam Moon Hyung Kyu Jun Tay Suh |
| author_sort | Minam Moon |
| collection | DOAJ |
| description | HDG method has been widely used as an effective numerical technique to obtain physically relevant solutions for PDE. In a practical setting, PDE comes with nonlinear coefficients. Hence, it is inevitable to consider how to obtain an approximate solution for PDE with nonlinear coefficients. Research on using HDG method for PDE with nonlinear coefficients has been conducted along with results obtained from computer simulations. However, error analysis on HDG method for such settings has been limited. In this research, we give error estimations of the hybridizable discontinuous Galerkin (HDG) method for parabolic equations with nonlinear coefficients. We first review the classical HDG method and define notions that will be used throughout the paper. Then, we will give bounds for our estimates when nonlinear coefficients obey “Lipschitz” condition. We will then prove our main result that the errors for our estimations are bounded. |
| format | Article |
| id | doaj-art-ca3808124dc043d28f2fd79bd446cf84 |
| institution | Kabale University |
| issn | 1687-9120 1687-9139 |
| language | English |
| publishDate | 2017-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Advances in Mathematical Physics |
| spelling | doaj-art-ca3808124dc043d28f2fd79bd446cf842025-02-03T01:26:40ZengWileyAdvances in Mathematical Physics1687-91201687-91392017-01-01201710.1155/2017/97368189736818Error Estimates on Hybridizable Discontinuous Galerkin Methods for Parabolic Equations with Nonlinear CoefficientsMinam Moon0Hyung Kyu Jun1Tay Suh2Department of Mathematics, Korea Military Academy, Hwarangro 564, Seoul 01805, Republic of KoreaDepartment of Mathematics, Korea Military Academy, Hwarangro 564, Seoul 01805, Republic of KoreaDepartment of Mathematics, Korea University, Anamro 145, Seoul 02841, Republic of KoreaHDG method has been widely used as an effective numerical technique to obtain physically relevant solutions for PDE. In a practical setting, PDE comes with nonlinear coefficients. Hence, it is inevitable to consider how to obtain an approximate solution for PDE with nonlinear coefficients. Research on using HDG method for PDE with nonlinear coefficients has been conducted along with results obtained from computer simulations. However, error analysis on HDG method for such settings has been limited. In this research, we give error estimations of the hybridizable discontinuous Galerkin (HDG) method for parabolic equations with nonlinear coefficients. We first review the classical HDG method and define notions that will be used throughout the paper. Then, we will give bounds for our estimates when nonlinear coefficients obey “Lipschitz” condition. We will then prove our main result that the errors for our estimations are bounded.http://dx.doi.org/10.1155/2017/9736818 |
| spellingShingle | Minam Moon Hyung Kyu Jun Tay Suh Error Estimates on Hybridizable Discontinuous Galerkin Methods for Parabolic Equations with Nonlinear Coefficients Advances in Mathematical Physics |
| title | Error Estimates on Hybridizable Discontinuous Galerkin Methods for Parabolic Equations with Nonlinear Coefficients |
| title_full | Error Estimates on Hybridizable Discontinuous Galerkin Methods for Parabolic Equations with Nonlinear Coefficients |
| title_fullStr | Error Estimates on Hybridizable Discontinuous Galerkin Methods for Parabolic Equations with Nonlinear Coefficients |
| title_full_unstemmed | Error Estimates on Hybridizable Discontinuous Galerkin Methods for Parabolic Equations with Nonlinear Coefficients |
| title_short | Error Estimates on Hybridizable Discontinuous Galerkin Methods for Parabolic Equations with Nonlinear Coefficients |
| title_sort | error estimates on hybridizable discontinuous galerkin methods for parabolic equations with nonlinear coefficients |
| url | http://dx.doi.org/10.1155/2017/9736818 |
| work_keys_str_mv | AT minammoon errorestimatesonhybridizablediscontinuousgalerkinmethodsforparabolicequationswithnonlinearcoefficients AT hyungkyujun errorestimatesonhybridizablediscontinuousgalerkinmethodsforparabolicequationswithnonlinearcoefficients AT taysuh errorestimatesonhybridizablediscontinuousgalerkinmethodsforparabolicequationswithnonlinearcoefficients |