A stabilizer free weak Galerkin method with implicit $θ$-schemes for fourth order parabolic problems
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arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866910308106240000 |
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| author | Gu, Shanshan Zhai, Qilong |
| author_facet | Gu, Shanshan Zhai, Qilong |
| contents | In this paper, we combine the stabilizer free weak Galerkin (SFWG) method and the implicit $θ$-schemes in time for $θ\in [\frac{1}{2},1]$ to solve the fourth-order parabolic problem. In particular, when $θ=1$, the full-discrete scheme is first-order backward Euler and the scheme is second-order Crank Nicolson scheme if $θ=\frac{1}{2}$. Next, we analyze the well-posedness of the schemes and deduce the optimal convergence orders of the error in the $H^2$ and $L^2$ norms. Finally, numerical examples confirm the theoretical results. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_14601 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A stabilizer free weak Galerkin method with implicit $θ$-schemes for fourth order parabolic problems Gu, Shanshan Zhai, Qilong Numerical Analysis In this paper, we combine the stabilizer free weak Galerkin (SFWG) method and the implicit $θ$-schemes in time for $θ\in [\frac{1}{2},1]$ to solve the fourth-order parabolic problem. In particular, when $θ=1$, the full-discrete scheme is first-order backward Euler and the scheme is second-order Crank Nicolson scheme if $θ=\frac{1}{2}$. Next, we analyze the well-posedness of the schemes and deduce the optimal convergence orders of the error in the $H^2$ and $L^2$ norms. Finally, numerical examples confirm the theoretical results. |
| title | A stabilizer free weak Galerkin method with implicit $θ$-schemes for fourth order parabolic problems |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2401.14601 |