Space-Time Isogeometric Method for a Nonlocal Parabolic Problem
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Acceso en línea: | |
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| _version_ | 1866911397744476160 |
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| author | Chaudhary, Sudhakar Chauhan, Shreya Montardini, Monica |
| author_facet | Chaudhary, Sudhakar Chauhan, Shreya Montardini, Monica |
| contents | In the present work, we focus on the space-time isogeometric discretization of a parabolic problem with a nonlocal diffusion coefficient. The existence and uniqueness of the solution for the continuous space-time variational formulation are proven. We prove the existence of the discrete solution and also establish the a priori error estimate for the space-time isogeometric scheme. The non-linear system is linearized through Picards method and a suitable preconditioner for the linearized system is provided. Finally, to confirm the theoretical findings, results of some numerical experiments are presented. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_00450 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Space-Time Isogeometric Method for a Nonlocal Parabolic Problem Chaudhary, Sudhakar Chauhan, Shreya Montardini, Monica Numerical Analysis In the present work, we focus on the space-time isogeometric discretization of a parabolic problem with a nonlocal diffusion coefficient. The existence and uniqueness of the solution for the continuous space-time variational formulation are proven. We prove the existence of the discrete solution and also establish the a priori error estimate for the space-time isogeometric scheme. The non-linear system is linearized through Picards method and a suitable preconditioner for the linearized system is provided. Finally, to confirm the theoretical findings, results of some numerical experiments are presented. |
| title | Space-Time Isogeometric Method for a Nonlocal Parabolic Problem |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2408.00450 |