Error estimates of $hp$-finite element method for elliptic optimal control problems with robin boundary
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2026
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866910003140493312 |
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| author | Lin, Xingyuan Lin, Xiuxiu Chen, Xuesong |
| author_facet | Lin, Xingyuan Lin, Xiuxiu Chen, Xuesong |
| contents | A priori and a posteriori error analysis of $hp$ finite element method for elliptic control problem with Robin boundary condition and boundary observation are presented. are presented. Through the Clément-type approach and the construction of an auxiliary system, we derived a priori error estimates for the elliptic optimal control problem. Residual-based a posteriori error estimates are derived based on the well-known Scott-Zhang-type quasi-interpolation and coupled state-control approximations, thus establishing an a posteriori error estimator for the $hp$ finite element method. The numerical example demonstrates the accuracy of error estimation for the elliptic optimal control problems with Robin boundary. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_20145 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Error estimates of $hp$-finite element method for elliptic optimal control problems with robin boundary Lin, Xingyuan Lin, Xiuxiu Chen, Xuesong Numerical Analysis Optimization and Control A priori and a posteriori error analysis of $hp$ finite element method for elliptic control problem with Robin boundary condition and boundary observation are presented. are presented. Through the Clément-type approach and the construction of an auxiliary system, we derived a priori error estimates for the elliptic optimal control problem. Residual-based a posteriori error estimates are derived based on the well-known Scott-Zhang-type quasi-interpolation and coupled state-control approximations, thus establishing an a posteriori error estimator for the $hp$ finite element method. The numerical example demonstrates the accuracy of error estimation for the elliptic optimal control problems with Robin boundary. |
| title | Error estimates of $hp$-finite element method for elliptic optimal control problems with robin boundary |
| topic | Numerical Analysis Optimization and Control |
| url | https://arxiv.org/abs/2601.20145 |