An $hp$ Error Analysis of HDG for Linear Fluid-Structure Interaction

Salim Meddahi

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arXiv · 2404.13578

An $hp$ Error Analysis of HDG for Linear Fluid-Structure Interaction

Salim Meddahi

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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 $hp$-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.

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Salim Meddahi. 2024-04-21. An $hp$ Error Analysis of HDG for Linear Fluid-Structure Interaction. https://arxiv.org/abs/2404.13578

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