An $hp$ Error Analysis of HDG for Linear Fluid-Structure Interaction
<|reference_start|>An $hp$ Error Analysis of HDG for Linear Fluid-Structure Interaction: A variational formulation based on velocity and stress is developed for linear fluid-structure interaction (FSI) problems. The well-posedness and energy stability of this formulation are established. To discretize the problem, a hybridizable discontinuous Galerkin method is employed. An $hp$-convergence analysis is performed for the resulting semi-discrete scheme. The temporal discretization is achieved via the Crank-Nicolson method, and the convergence properties of the fully discrete scheme are examined. Numerical experiments validate the theoretical results, confirming the effectiveness and accuracy of the proposed method.<|reference_end|>
@article{meddahi2024an,
    title={An $hp$ Error Analysis of HDG for Linear Fluid-Structure Interaction},
    author={Salim Meddahi},
    journal={arXiv preprint arXiv:2404.13578},
    year={2024},
    archivePrefix={arXiv},
    eprint={2404.13578},
    primaryClass={math.NA cs.NA}
}