A reconstructed discontinuous approximation for distributed elliptic control problems
Fuente:
arXiv
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866909979592622080 |
|---|---|
| author | Li, Ruo Liu, Haoyang Yin, Jun |
| author_facet | Li, Ruo Liu, Haoyang Yin, Jun |
| contents | In this paper, we present and analyze an interior penalty discontinuous Galerkin method for the distributed elliptic optimal control problems. It is based on a reconstructed discontinuous approximation which admits arbitrarily high-order approximation space with only one unknown per element. Applying this method, we develop a proper discretization scheme that approximates the state and adjoint variables in the approximation space. Our main contributions are twofold: (1) the derivation of both a priori and a posteriori error estimates of the $L^2$-norm and the energy norms, and (2) the implementation of an efficiently solvable discrete system, which is solved via a linearly convergent projected gradient descent method. Numerical experiments are provided to verify the convergence order in a priori error estimate and the efficiency of a posteriori error estimate. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_08353 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A reconstructed discontinuous approximation for distributed elliptic control problems Li, Ruo Liu, Haoyang Yin, Jun Numerical Analysis Optimization and Control In this paper, we present and analyze an interior penalty discontinuous Galerkin method for the distributed elliptic optimal control problems. It is based on a reconstructed discontinuous approximation which admits arbitrarily high-order approximation space with only one unknown per element. Applying this method, we develop a proper discretization scheme that approximates the state and adjoint variables in the approximation space. Our main contributions are twofold: (1) the derivation of both a priori and a posteriori error estimates of the $L^2$-norm and the energy norms, and (2) the implementation of an efficiently solvable discrete system, which is solved via a linearly convergent projected gradient descent method. Numerical experiments are provided to verify the convergence order in a priori error estimate and the efficiency of a posteriori error estimate. |
| title | A reconstructed discontinuous approximation for distributed elliptic control problems |
| topic | Numerical Analysis Optimization and Control |
| url | https://arxiv.org/abs/2512.08353 |