An unconditionally stable space-time isogeometric method for a biharmonic wave equation
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866913002087776256 |
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| author | Chauhan, S. Chaudhary, S. |
| author_facet | Chauhan, S. Chaudhary, S. |
| contents | This work presents a space-time isogeometric analysis of biharmonic wave problem, in contrast to the more common application of space-time methods to second order wave equations. We first establish the unique solvability of the continuous space-time variational formulation. In order to obtain $H^2$- conforming discretization of the biharmonic wave equation, we consider globally smooth B-spline functions having continuity higher than $C^0$. We prove that the resulting space-time discrete formulation is stable under a Courant-Friedrichs-Lewy (CFL) condition. Furthermore, we propose a stabilized formulation, achieved by adding a non-consistent penalty term, which yields unconditional stability. Exploiting the tensor product structure, an efficient direct solver is also provided for solving the linear system arising from the discrete formulation. A few numerical experiments are presented to demonstrate the stability and convergence properties of the proposed scheme as well as the efficiency of the proposed solver. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_03109 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | An unconditionally stable space-time isogeometric method for a biharmonic wave equation Chauhan, S. Chaudhary, S. Numerical Analysis This work presents a space-time isogeometric analysis of biharmonic wave problem, in contrast to the more common application of space-time methods to second order wave equations. We first establish the unique solvability of the continuous space-time variational formulation. In order to obtain $H^2$- conforming discretization of the biharmonic wave equation, we consider globally smooth B-spline functions having continuity higher than $C^0$. We prove that the resulting space-time discrete formulation is stable under a Courant-Friedrichs-Lewy (CFL) condition. Furthermore, we propose a stabilized formulation, achieved by adding a non-consistent penalty term, which yields unconditional stability. Exploiting the tensor product structure, an efficient direct solver is also provided for solving the linear system arising from the discrete formulation. A few numerical experiments are presented to demonstrate the stability and convergence properties of the proposed scheme as well as the efficiency of the proposed solver. |
| title | An unconditionally stable space-time isogeometric method for a biharmonic wave equation |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2604.03109 |