Semi and fully-discrete analysis of lowest-order nonstandard finite element methods for the biharmonic wave problem
<|reference_start|>Semi and fully-discrete analysis of lowest-order nonstandard finite element methods for the biharmonic wave problem: 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 $H^2_0(\Omega)$ 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.<|reference_end|>
@article{nataraj2024semi,
    title={Semi and fully-discrete analysis of lowest-order nonstandard finite
  element methods for the biharmonic wave problem},
    author={Neela Nataraj, Ricardo Ruiz-Baier, and Aamir Yousuf},
    journal={arXiv preprint arXiv:2407.03777},
    year={2024},
    archivePrefix={arXiv},
    eprint={2407.03777},
    primaryClass={math.NA cs.NA}
}