A strong two-stage explicit/implicit approach combined with mixed finite element methods for a three-dimensional nonlinear radiation-conduction model in anisotropic media
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arXiv
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866911346344329216 |
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| author | Ngondiep, Eric |
| author_facet | Ngondiep, Eric |
| contents | This paper develops a strong computational approach to simulate a three-dimensional nonlinear radiation-conduction model in optically thick media, subject to suitable initial and boundary conditions. The space derivatives are approximated by the mixed finite element method ($\mathcal{P}_{p}/\mathcal{P}_{p-1}$), while the interpolation technique is employed in two stages to approximate the time derivative. The proposed strategy is so-called, a strong two-stage explicit/implicit computational technique combined with mixed finite element method. Specifically, the new algorithm should be observed as a predictor-corrector numerical scheme. Additionally, it efficiently treats the time derivative term and provides a necessary requirement on time step for stability. Under this time step limitation, the stability is deeply analyzed whereas the convergence order is numerically computed in the $L^{2}$-norm. The theoretical results suggest that the developed approach is stable and temporal second-order accurate. Some numerical experiments are performed to confirm the theory, to establish that the constructed method is spatial fourth-order convergent and to demonstrate the practical applicability and computational efficiency of the numerical scheme. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_06456 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A strong two-stage explicit/implicit approach combined with mixed finite element methods for a three-dimensional nonlinear radiation-conduction model in anisotropic media Ngondiep, Eric Numerical Analysis 65M12, 65M06 This paper develops a strong computational approach to simulate a three-dimensional nonlinear radiation-conduction model in optically thick media, subject to suitable initial and boundary conditions. The space derivatives are approximated by the mixed finite element method ($\mathcal{P}_{p}/\mathcal{P}_{p-1}$), while the interpolation technique is employed in two stages to approximate the time derivative. The proposed strategy is so-called, a strong two-stage explicit/implicit computational technique combined with mixed finite element method. Specifically, the new algorithm should be observed as a predictor-corrector numerical scheme. Additionally, it efficiently treats the time derivative term and provides a necessary requirement on time step for stability. Under this time step limitation, the stability is deeply analyzed whereas the convergence order is numerically computed in the $L^{2}$-norm. The theoretical results suggest that the developed approach is stable and temporal second-order accurate. Some numerical experiments are performed to confirm the theory, to establish that the constructed method is spatial fourth-order convergent and to demonstrate the practical applicability and computational efficiency of the numerical scheme. |
| title | A strong two-stage explicit/implicit approach combined with mixed finite element methods for a three-dimensional nonlinear radiation-conduction model in anisotropic media |
| topic | Numerical Analysis 65M12, 65M06 |
| url | https://arxiv.org/abs/2512.06456 |