Pre-Publicación 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 C^2 boundary ∂Ω. The computational domain Ωh does not necessarily fit Ω, and the Transfer Path Method (TPM) is employed to transfer the boundary data from ∂Ω to ∂Ωh along segments in the direction m. Under suitable closeness assumptions between ∂Ωh and ∂Ω, as well as on the transfer vector m, we prove optimal-order convergence in the L²-norm for all variables of both the state and adjoint problems. Numerical experiments are also presented to support the theoretical results.
