Adaptive finite element methods optimal control governed by PDEs
ADAPTIVE FINITE ELEMENT METHODS: Optimal Control Governed by PDEs emphasizes the discussions of some unique issues from the adaptive finite element approximation of optimal control. The main idea used in the approximation error analysis (both a priori and a posteriori) is to first combine convex ana...
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| Other Authors: | |
| Format: | Book |
| Language: | English |
| Published: |
Beijing, China Oxford
Science Press Alpha Science International
2012
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| Series: | Series in information and computational science
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| 001 | 49884 | ||
| 003 | MY-KLNDU | ||
| 005 | 20241219005837.0 | ||
| 008 | 131005s2012 cc a b 000 0 eng d | ||
| 020 | |a 9781842657157 (alpha science) | ||
| 020 | |a 1842657151 (alpha science) | ||
| 039 | 9 | |a 201404141419 |b zul |c 201311261212 |d shahrim |y 201310051553 |z aiza | |
| 040 | |a UPNM | ||
| 090 | |a TA 347 .F5 |b .L58 2012 | ||
| 100 | 1 | |a Liu, Wenbin | |
| 245 | 1 | 0 | |a Adaptive finite element methods |b optimal control governed by PDEs |c Wenbin Liu, Ningning Yan |
| 260 | |a Beijing, China |b Science Press |a Oxford |b Alpha Science International |c 2012 | ||
| 300 | |a viii, 197 p. |b ill. |c 25 cm | ||
| 490 | 1 | |a Series in information and computational science | |
| 504 | |a Includes bibliographical references. | ||
| 505 | 0 | |a Ch 1. Introduction -- Ch 2. Existence and Optimality Conditions of Optimal Control -- Ch 3. Finite Element Approximation of Optimal Control -- Ch 4. A Priori Error Estimates for Optimal Control (I) -- Ch 5. A Priori Error Estimates for Optimal Control (II) -- Ch 6. Adaptivity Finite Element Method for Optimal Control -- Ch 7. A Posteriori Error Estimates for Optimal Control -- Ch 8. Numerical Computations of Optimal Control -- Ch 9. Recovery Based a Posteriori Error Estimators -- Ch 10. Adaptive Mixed Finite Element Method for Optimal Control -- Bibliography | |
| 520 | |a ADAPTIVE FINITE ELEMENT METHODS: Optimal Control Governed by PDEs emphasizes the discussions of some unique issues from the adaptive finite element approximation of optimal control. The main idea used in the approximation error analysis (both a priori and a posteriori) is to first combine convex analysis and interpolation error estimations of suitable interpolators, which depend on the structure of the control constraints, to derive the error estimates for the control via the variational inequalities in the optimality conditions, and then to apply the standard techniques to derive the error estimates for the state equations. The need, the framework and the techniques of using multi adaptive meshes in developing efficient numerical algorithms for optimal control have been emphasized throughout the book. The book starts from several typical examples of optimal control problems and then discusses existence and optimality conditions for some optimal control problems. Then the finite element approximation schemes for several typical optimal control problems are set up, their a priori and a posteriori error estimates are derived following the main idea mentioned, and their computational methods are studied. | ||
| 592 | |a 00012621 |b 31/10/2013 |c RM211.48 |h PVK | ||
| 650 | 0 | |a Finite element method. | |
| 650 | 0 | |a Differential equations, partial |x Numerical solutions. | |
| 700 | 1 | |a Yan, Ningning | |
| 830 | 0 | |a Series in information and computational science | |
| 999 | |a vtls000050539 |c 49884 |d 49884 | ||