Semi and fully-discrete analysis of lowest-order nonstandard finite element methods for the biharmonic wave problem
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866911056469688320 |
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| author | Nataraj, Neela Ruiz-Baier, Ricardo Yousuf, Aamir |
| author_facet | Nataraj, Neela Ruiz-Baier, Ricardo Yousuf, Aamir |
| contents | This paper discusses lowest-order nonstandard finite element methods for space discretization and explicit and implicit schemes for time discretization of the biharmonic wave equation with clamped boundary conditions. A modified Ritz projection operator defined on $H^2_0(Ω)$ ensures error estimates under appropriate regularity assumptions on the solution. Stability results and error estimates of optimal order are established in suitable norms for the semidiscrete and explicit/implicit fully-discrete versions of the proposed schemes. Finally, we report on numerical experiments using explicit and implicit schemes for time discretization and Morley, discontinuous Galerkin, and {C$^0$ interior} penalty schemes for space discretization, that validate the theoretical error estimates. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_03777 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Semi and fully-discrete analysis of lowest-order nonstandard finite element methods for the biharmonic wave problem Nataraj, Neela Ruiz-Baier, Ricardo Yousuf, Aamir Numerical Analysis This paper discusses lowest-order nonstandard finite element methods for space discretization and explicit and implicit schemes for time discretization of the biharmonic wave equation with clamped boundary conditions. A modified Ritz projection operator defined on $H^2_0(Ω)$ ensures error estimates under appropriate regularity assumptions on the solution. Stability results and error estimates of optimal order are established in suitable norms for the semidiscrete and explicit/implicit fully-discrete versions of the proposed schemes. Finally, we report on numerical experiments using explicit and implicit schemes for time discretization and Morley, discontinuous Galerkin, and {C$^0$ interior} penalty schemes for space discretization, that validate the theoretical error estimates. |
| title | Semi and fully-discrete analysis of lowest-order nonstandard finite element methods for the biharmonic wave problem |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2407.03777 |