Low Regularity Primal-Dual Weak Galerkin Finite Element Methods for Convection-Diffusion Equations
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2019
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| _version_ | 1866909434925547520 |
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| author | Wang, Chunmei Zikatanov, Ludmil |
| author_facet | Wang, Chunmei Zikatanov, Ludmil |
| contents | We propose a numerical method for convection-diffusion problems under low regularity assumptions. We derive the method and analyze it using the primal-dual weak Galerkin (PDWG) finite element framework. The Euler-Lagrange formulation resulting from the PDWG scheme yields a system of equations involving not only the equation for the primal variable but also its adjoint for the dual variable. We show that the proposed PDWG method is stable and convergent. We also derive a priori error estimates for the primal variable in the $H^ε$-norm for $ε\in [0,\frac12)$. A series of numerical tests that validate the theory and are presented as well. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1901_06743 |
| institution | arXiv |
| publishDate | 2019 |
| record_format | arxiv |
| spellingShingle | Low Regularity Primal-Dual Weak Galerkin Finite Element Methods for Convection-Diffusion Equations Wang, Chunmei Zikatanov, Ludmil Numerical Analysis 65N30, 65N15, 65N12, 74N20 We propose a numerical method for convection-diffusion problems under low regularity assumptions. We derive the method and analyze it using the primal-dual weak Galerkin (PDWG) finite element framework. The Euler-Lagrange formulation resulting from the PDWG scheme yields a system of equations involving not only the equation for the primal variable but also its adjoint for the dual variable. We show that the proposed PDWG method is stable and convergent. We also derive a priori error estimates for the primal variable in the $H^ε$-norm for $ε\in [0,\frac12)$. A series of numerical tests that validate the theory and are presented as well. |
| title | Low Regularity Primal-Dual Weak Galerkin Finite Element Methods for Convection-Diffusion Equations |
| topic | Numerical Analysis 65N30, 65N15, 65N12, 74N20 |
| url | https://arxiv.org/abs/1901.06743 |