{"ID":2831089,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2512.08353","arxiv_id":"2512.08353","title":"A reconstructed discontinuous approximation for distributed elliptic control problems","abstract":"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.","short_abstract":"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 de...","url_abs":"https://arxiv.org/abs/2512.08353","url_pdf":"https://arxiv.org/pdf/2512.08353v2","authors":"[\"Ruo Li\",\"Haoyang Liu\",\"Jun Yin\"]","published":"2025-12-09T08:27:25Z","proceeding":"math.NA","tasks":"[\"math.NA\",\"math.OC\"]","methods":"[]","has_code":false}