A reconstructed discontinuous approximation for distributed elliptic control problems Article Swipe
In this paper, we present and analyze an internal 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 estimate and the efficiency of a posteriori error estimate.
Related Topics
Concepts
Mathematics
A priori and a posteriori
Discretization
Convergence (economics)
Applied mathematics
Approximation error
Discontinuous Galerkin method
Gradient descent
Optimal control
Galerkin method
Approximation theory
Space (punctuation)
Mathematical analysis
Scheme (mathematics)
Mathematical optimization
Adjoint equation
Error detection and correction
Approximation algorithm
Descent (aeronautics)
Energy (signal processing)
Elliptic curve
Iterative method
Gradient method
Discretization error
A priori estimate
Rate of convergence
State space
State (computer science)
Metadata
- Type
- article
- Landing Page
- http://arxiv.org/abs/2512.08353
- https://arxiv.org/pdf/2512.08353
- OA Status
- green
- OpenAlex ID
- https://openalex.org/W7114820829
All OpenAlex metadata
Raw OpenAlex JSON
- OpenAlex ID
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https://openalex.org/W7114820829Canonical identifier for this work in OpenAlex
- Title
-
A reconstructed discontinuous approximation for distributed elliptic control problemsWork title
- Type
-
articleOpenAlex work type
- Publication year
-
2025Year of publication
- Publication date
-
2025-12-09Full publication date if available
- Authors
-
Li, Ruo, Liu, Haoyang, Yin, JunList of authors in order
- Landing page
-
https://arxiv.org/abs/2512.08353Publisher landing page
- PDF URL
-
https://arxiv.org/pdf/2512.08353Direct link to full text PDF
- Open access
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YesWhether a free full text is available
- OA status
-
greenOpen access status per OpenAlex
- OA URL
-
https://arxiv.org/pdf/2512.08353Direct OA link when available
- Concepts
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Mathematics, A priori and a posteriori, Discretization, Convergence (economics), Applied mathematics, Approximation error, Discontinuous Galerkin method, Gradient descent, Optimal control, Galerkin method, Approximation theory, Space (punctuation), Mathematical analysis, Scheme (mathematics), Mathematical optimization, Adjoint equation, Error detection and correction, Approximation algorithm, Descent (aeronautics), Energy (signal processing), Elliptic curve, Iterative method, Gradient method, Discretization error, A priori estimate, Rate of convergence, State space, State (computer science)Top concepts (fields/topics) attached by OpenAlex
- Cited by
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0Total citation count in OpenAlex
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| citation_normalized_percentile.is_in_top_1_percent | False |
| citation_normalized_percentile.is_in_top_10_percent | False |