An hp Error Analysis of HDG for Linear Fluid–Structure Interaction

Abstract

A variational formulation based on velocity and stress is developed for linear fluid–structure interaction problems. The well-posedness and energy stability of this formulation are established. A hybridizable discontinuous Galerkin method is employed to discretize the problem. An hp-convergence analysis is performed for the resulting semi-discrete scheme. The Crank–Nicolson method is used for temporal discretization, and the convergence properties of the fully discrete scheme are examined. Numerical experiments are presented to validate the theoretical results and demonstrate the accuracy of the proposed method.