Pre-Publicación 2026-35
Isaac Bermudez, Jaime Manríquez, Manuel Solano:
Analysis of an unfitted HDG method for the coupled linear elasticity/Stokes problem
Abstract:
This work analyzes a Hybridizable discontinuous Galerkin (HDG) method for the fluid/structure interaction problem, where the computational domain does not necessarily fit the interface. We consider a steady-state system arising from the time discretization of a Stokes fluid interacting with a linear elastic solid. We employ the transfer path method to impose the transmission conditions of the fluid velocity and displacement of the solid, and the continuity of the normal component of the stress tensor is approximated by local extrapolations of their polynomial approximation. Under certain assumptions, we prove that the theoretical order of convergence of the error in L^2-norm is, at least, h^k for all the variables, where h is the meshsize and k the polynomial degree of the HDG spaces, and we identify the specific gap conditions required to recover quasi-optimal or optimal rates. We present numerical experiments supporting the theory, as well as results for a benchmark fluid-structure interaction problem solving the incompressible Navier–Stokes equations.
