A priori error estimates of finite volume methods for general elliptic optimal control problems
| dc.contributor.author | Feng, Yuming | |
| dc.contributor.author | Lu, Zuliang | |
| dc.contributor.author | Cao, Longzhou | |
| dc.contributor.author | Li, Lin | |
| dc.contributor.author | Zhang, Shuhua | |
| dc.date.accessioned | 2022-08-17T15:47:17Z | |
| dc.date.available | 2022-08-17T15:47:17Z | |
| dc.date.issued | 2017-10-27 | |
| dc.description.abstract | In this article, we establish a priori error estimates for the finite volume approximation of general elliptic optimal control problems. We use finite volume methods to discretize the state and adjoint equation of the optimal control problems. For the variational inequality, we use the variational discretization methods to discretize the control. We show the existence and the uniqueness of the solution for discrete optimality conditions. Under some reasonable assumptions, we obtain some optimal order error estimates for the state, costate and control variables. On one hand, the convergence rate for the state, costate and control variables is O(h2) or O(h2 ā|log(1/h)|) in the sense of L2 norm or Lā norm. On the other hand, the convergence rate for the state and costate variables is O(h) or O(h|log(1/h)|) in the sense of H1 norm or W1,ā norm. | |
| dc.description.department | Mathematics | |
| dc.format | Text | |
| dc.format.extent | 15 pages | |
| dc.format.medium | 1 file (.pdf) | |
| dc.identifier.citation | Feng, Y., Lu, Z., Cao, L., Li, L., & Zhang, S. (2017). A priori error estimates of finite volume methods for general elliptic optimal control problems. <i>Electronic Journal of Differential Equations, 2017</i>(267), pp. 1-15. | |
| dc.identifier.issn | 1072-6691 | |
| dc.identifier.uri | https://hdl.handle.net/10877/16068 | |
| dc.language.iso | en | |
| dc.publisher | Texas State University, Department of Mathematics | |
| dc.rights | Attribution 4.0 International | |
| dc.rights.uri | https://creativecommons.org/licenses/by/4.0/ | |
| dc.source | Electronic Journal of Differential Equations, 2017, San Marcos, Texas: Texas State University and University of North Texas. | |
| dc.subject | A priori error estimates | |
| dc.subject | General elliptic optimal control problems | |
| dc.subject | Finite volume methods | |
| dc.subject | Optimal-order | |
| dc.title | A priori error estimates of finite volume methods for general elliptic optimal control problems | |
| dc.type | Article |