An unfitted HDG method for a distributed optimal convection-diffusion control problem
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2026
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866908927983091712 |
|---|---|
| author | Henríquez, Esteban Solano, Manuel |
| author_facet | Henríquez, Esteban Solano, Manuel |
| contents | 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 piecewise-wise $\mathcal{C}^2$ boundary $\partial Ω$. The computational domain $Ω_h$ does not necessarily fit $Ω$ and the Transfer Path Method (TPM) is used to transfer the boundary data from $\partial Ω$ to $\partial Ω_h$ through segments of direction $\boldsymbol{m}$. Under closeness conditions between $\partial Ω_h$ and $\partial Ω$ and on the transfer vector $\boldsymbol{m}$, 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_00211 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | An unfitted HDG method for a distributed optimal convection-diffusion control problem Henríquez, Esteban Solano, Manuel Numerical Analysis 65M60, 49M41 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 piecewise-wise $\mathcal{C}^2$ boundary $\partial Ω$. The computational domain $Ω_h$ does not necessarily fit $Ω$ and the Transfer Path Method (TPM) is used to transfer the boundary data from $\partial Ω$ to $\partial Ω_h$ through segments of direction $\boldsymbol{m}$. Under closeness conditions between $\partial Ω_h$ and $\partial Ω$ and on the transfer vector $\boldsymbol{m}$, 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. |
| title | An unfitted HDG method for a distributed optimal convection-diffusion control problem |
| topic | Numerical Analysis 65M60, 49M41 |
| url | https://arxiv.org/abs/2604.00211 |