Finite Element Approximation of Optimal Control Problem with Weighted Extended B-Splines
In this research article, an optimal control problem (OCP) with boundary observations is approximated using finite element method (FEM) with weighted extended B-splines (WEB-splines) as basis functions. This type of OCP has a distinct aspect that the boundary observations are outward normal derivati...
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2019-05-01
|
| Series: | Mathematics |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2227-7390/7/5/452 |
| _version_ | 1818672185386991616 |
|---|---|
| author | Madiha Sana Muhammad Mustahsan |
| author_facet | Madiha Sana Muhammad Mustahsan |
| author_sort | Madiha Sana |
| collection | DOAJ |
| description | In this research article, an optimal control problem (OCP) with boundary observations is approximated using finite element method (FEM) with weighted extended B-splines (WEB-splines) as basis functions. This type of OCP has a distinct aspect that the boundary observations are outward normal derivatives of state variables, which decrease the regularity of solution. A meshless FEM is proposed using WEB-splines, defined on the usual grid over the domain, <inline-formula> <math display="inline"> <semantics> <msup> <mi mathvariant="double-struck">R</mi> <mn>2</mn> </msup> </semantics> </math> </inline-formula>. The weighted extended B-spline method (WEB method) absorbs the regularity problem as the degree of the B-splines is increased. Convergence analysis is also performed by some numerical examples. |
| first_indexed | 2024-12-17T07:35:53Z |
| format | Article |
| id | doaj.art-2526fae2e79f449e9ef527510b137f73 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-12-17T07:35:53Z |
| publishDate | 2019-05-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-2526fae2e79f449e9ef527510b137f732022-12-21T21:58:19ZengMDPI AGMathematics2227-73902019-05-017545210.3390/math7050452math7050452Finite Element Approximation of Optimal Control Problem with Weighted Extended B-SplinesMadiha Sana0Muhammad Mustahsan1Department of Mathematics, The Islamia University of Bahawalpur, Bahawalpur 63100, PakistanDepartment of Mathematics, The Islamia University of Bahawalpur, Bahawalpur 63100, PakistanIn this research article, an optimal control problem (OCP) with boundary observations is approximated using finite element method (FEM) with weighted extended B-splines (WEB-splines) as basis functions. This type of OCP has a distinct aspect that the boundary observations are outward normal derivatives of state variables, which decrease the regularity of solution. A meshless FEM is proposed using WEB-splines, defined on the usual grid over the domain, <inline-formula> <math display="inline"> <semantics> <msup> <mi mathvariant="double-struck">R</mi> <mn>2</mn> </msup> </semantics> </math> </inline-formula>. The weighted extended B-spline method (WEB method) absorbs the regularity problem as the degree of the B-splines is increased. Convergence analysis is also performed by some numerical examples.https://www.mdpi.com/2227-7390/7/5/452finite element methodWEB-splinesoptimal control problemB-splineweight function |
| spellingShingle | Madiha Sana Muhammad Mustahsan Finite Element Approximation of Optimal Control Problem with Weighted Extended B-Splines Mathematics finite element method WEB-splines optimal control problem B-spline weight function |
| title | Finite Element Approximation of Optimal Control Problem with Weighted Extended B-Splines |
| title_full | Finite Element Approximation of Optimal Control Problem with Weighted Extended B-Splines |
| title_fullStr | Finite Element Approximation of Optimal Control Problem with Weighted Extended B-Splines |
| title_full_unstemmed | Finite Element Approximation of Optimal Control Problem with Weighted Extended B-Splines |
| title_short | Finite Element Approximation of Optimal Control Problem with Weighted Extended B-Splines |
| title_sort | finite element approximation of optimal control problem with weighted extended b splines |
| topic | finite element method WEB-splines optimal control problem B-spline weight function |
| url | https://www.mdpi.com/2227-7390/7/5/452 |
| work_keys_str_mv | AT madihasana finiteelementapproximationofoptimalcontrolproblemwithweightedextendedbsplines AT muhammadmustahsan finiteelementapproximationofoptimalcontrolproblemwithweightedextendedbsplines |