An $hp$ Error Analysis of HDG for Linear Fluid-Structure Interaction
Numerical Analysis
2024-04-23 v1 Numerical Analysis
Abstract
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 -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.
Cite
@article{arxiv.2404.13578,
title = {An $hp$ Error Analysis of HDG for Linear Fluid-Structure Interaction},
author = {Salim Meddahi},
journal= {arXiv preprint arXiv:2404.13578},
year = {2024}
}