| Title:
|
New a posteriori $L^{\infty }(L^2) $ and $L^2(L^2)$-error estimates of mixed finite element methods for general nonlinear parabolic optimal control problems (English) |
| Author:
|
Lu, Zuliang |
| Language:
|
English |
| Journal:
|
Applications of Mathematics |
| ISSN:
|
0862-7940 (print) |
| ISSN:
|
1572-9109 (online) |
| Volume:
|
61 |
| Issue:
|
2 |
| Year:
|
2016 |
| Pages:
|
135-163 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We study new a posteriori error estimates of the mixed finite element methods for general optimal control problems governed by nonlinear parabolic equations. The state and the co-state are discretized by the high order Raviart-Thomas mixed finite element spaces and the control is approximated by piecewise constant functions. We derive a posteriori error estimates in $L^{\infty }(J;L^2(\Omega )) $-norm and $L^2(J;L^2(\Omega ))$-norm for both the state, the co-state and the control approximation. Such estimates, which seem to be new, are an important step towards developing a reliable adaptive mixed finite element approximation for optimal control problems. Finally, the performance of the posteriori error estimators is assessed by two numerical examples. (English) |
| Keyword:
|
a posteriori error estimate |
| Keyword:
|
general optimal control problem |
| Keyword:
|
nonlinear parabolic equation |
| Keyword:
|
mixed finite element method |
| MSC:
|
49J20 |
| MSC:
|
65N30 |
| idZBL:
|
Zbl 06562151 |
| idMR:
|
MR3470771 |
| DOI:
|
10.1007/s10492-016-0126-x |
| . |
| Date available:
|
2016-03-17T19:30:50Z |
| Last updated:
|
2020-07-02 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/144842 |
| . |
| Reference:
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