內容簡介
本書主要介紹了幾類很優控制問題的高效算法,包括了橢圓很優控制問題、拋物很優控制問題、雙曲很優控制問題、四階很優控制問題等新近熱門領域,結合了作者本人在很優控制問題方面的研究成果,並根據作者方法、變分離散方法、混方法、有限體積法和譜方法的理解和研究生教學要求,全面、客觀的評價了這幾類很優控制問題的數值計算方法,並列舉了很多數值算例,闡述了許多新的學術觀點,具有較大的學術價值。
●Chapter 1 Introduction
●Chapter 2 Some preliminaries
●2.1 Sobolev spaces
●2.2 Finite element methods for elliptic equations
●2.2.1 A priori error estimates
●2.2.2 A posteriori error estimates
●2.2.3 Superconvergence
●2.3 Mixed finite element methods
●2.3.1 Elliptic equations
●2.3.2 Parabolic equations
●2.3.3 Hyperbolic equations
●2.4 Optimal control problems
●2.4.1 Backgrounds and motivations
●2.4.2 Some typical examples
●2.4.3 Optimality conditions
●Chapter 3 Finite element methods for optimal control problems
●3.1 Elliptic optimal control problems
●3.1.1 Distributed elliptic optimal control problems
●3.1.2 Finite element discretization
●3.1.3 A posteriori error estimates......