Convergence analysis of a dual-wind discontinuous Galerkin method for an elliptic optimal control problem with control constraints
This paper investigates a symmetric dual-wind discontinuous Galerkin (DWDG) method for solving an elliptic optimal control problem with control constraints. The governing constraint is an elliptic partial differential equation (PDE), which is discretized using the symmetric DWDG approach. We derive...
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| Format: | Article |
| Language: | English |
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Elsevier
2025-08-01
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| Series: | Results in Applied Mathematics |
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| Online Access: | http://www.sciencedirect.com/science/article/pii/S2590037425000883 |
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| author | Satyajith Bommana Boyana Thomas Lewis Sijing Liu Yi Zhang |
| author_facet | Satyajith Bommana Boyana Thomas Lewis Sijing Liu Yi Zhang |
| author_sort | Satyajith Bommana Boyana |
| collection | DOAJ |
| description | This paper investigates a symmetric dual-wind discontinuous Galerkin (DWDG) method for solving an elliptic optimal control problem with control constraints. The governing constraint is an elliptic partial differential equation (PDE), which is discretized using the symmetric DWDG approach. We derive error estimates in the energy norm for both the state and the adjoint state, as well as in the L2 norm of the control variable. Numerical experiments are provided to demonstrate the robustness and effectiveness of the developed scheme. |
| format | Article |
| id | doaj-art-bb52ace02aeb45dc8976abb8b5894ff3 |
| institution | Kabale University |
| issn | 2590-0374 |
| language | English |
| publishDate | 2025-08-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Results in Applied Mathematics |
| spelling | doaj-art-bb52ace02aeb45dc8976abb8b5894ff32025-08-20T04:02:51ZengElsevierResults in Applied Mathematics2590-03742025-08-012710062410.1016/j.rinam.2025.100624Convergence analysis of a dual-wind discontinuous Galerkin method for an elliptic optimal control problem with control constraintsSatyajith Bommana Boyana0Thomas Lewis1Sijing Liu2Yi Zhang3Department of Applied Mathematics, Florida Polytechnic University, Lakeland, FL, USA; Corresponding author.Department of Mathematics and Statistics, The University of North Carolina at Greensboro, Greensboro, NC, USADepartment of Mathematical Sciences, Worcester Polytechnic Institute, Worcester, MA, USADepartment of Mathematics and Statistics, The University of North Carolina at Greensboro, Greensboro, NC, USAThis paper investigates a symmetric dual-wind discontinuous Galerkin (DWDG) method for solving an elliptic optimal control problem with control constraints. The governing constraint is an elliptic partial differential equation (PDE), which is discretized using the symmetric DWDG approach. We derive error estimates in the energy norm for both the state and the adjoint state, as well as in the L2 norm of the control variable. Numerical experiments are provided to demonstrate the robustness and effectiveness of the developed scheme.http://www.sciencedirect.com/science/article/pii/S2590037425000883Elliptic optimal control problemBox constraintsDiscontinuous Galerkin methodsDual-wind DG methodsA priori error analysis |
| spellingShingle | Satyajith Bommana Boyana Thomas Lewis Sijing Liu Yi Zhang Convergence analysis of a dual-wind discontinuous Galerkin method for an elliptic optimal control problem with control constraints Results in Applied Mathematics Elliptic optimal control problem Box constraints Discontinuous Galerkin methods Dual-wind DG methods A priori error analysis |
| title | Convergence analysis of a dual-wind discontinuous Galerkin method for an elliptic optimal control problem with control constraints |
| title_full | Convergence analysis of a dual-wind discontinuous Galerkin method for an elliptic optimal control problem with control constraints |
| title_fullStr | Convergence analysis of a dual-wind discontinuous Galerkin method for an elliptic optimal control problem with control constraints |
| title_full_unstemmed | Convergence analysis of a dual-wind discontinuous Galerkin method for an elliptic optimal control problem with control constraints |
| title_short | Convergence analysis of a dual-wind discontinuous Galerkin method for an elliptic optimal control problem with control constraints |
| title_sort | convergence analysis of a dual wind discontinuous galerkin method for an elliptic optimal control problem with control constraints |
| topic | Elliptic optimal control problem Box constraints Discontinuous Galerkin methods Dual-wind DG methods A priori error analysis |
| url | http://www.sciencedirect.com/science/article/pii/S2590037425000883 |
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