Preprint 2026-11
Esteban Henriquez, Manuel Solano:
An unfitted HDG method for a distributed optimal convection-diffusion control problem
Abstract:
We analyze a high-order unfitted hybridizable discontinuous Galerkin (HDG) method for an optimal control problem governed by a convection–diffusion equation posed in a domain with a piecewise-wise $mathcal{C}^2$ boundary ∂Ω. The computational domain Ω_h does not necessarily fit Ω, and the Transfer Path Method (TPM) is used to transfer the boundary data from ∂Ω to ∂Ω_h through segments in the direction m. Under closeness conditions between ∂Ω_h and ∂Ω, and on the transfer vector m, we prove optimal order of convergence in the $L^2$-norm for all variables of the state and adjoint problems. We also show numerical examples to complement the theory.
