Abstract
In this chapter we will introduce the basic concepts of optimal control for linear elliptic partial differential equations. At first we present the classical theory in functional spaces “à la J.L.Lions”, see [Lio71, Lio72]; then we will address the methodology based on the use of the Lagrangian functional (see, e.g., [Mau81, BKR00, Jam88]). Finally, we will show two different numerical approaches for control problems, based on the Galerkin finite element method.
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© 2014 Springer-Verlag Italia
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Quarteroni, A. (2014). Optimal control of partial differential equations. In: Numerical Models for Differential Problems. MS&A - Modeling, Simulation and Applications, vol 8. Springer, Milano. https://doi.org/10.1007/978-88-470-5522-3_17
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DOI: https://doi.org/10.1007/978-88-470-5522-3_17
Publisher Name: Springer, Milano
Print ISBN: 978-88-470-5521-6
Online ISBN: 978-88-470-5522-3
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