Goals Theory A priori A priori error estimates N1 bound various“ measures” of u exact]-un [approximate] in terms of C(n, problem parameters h [mesh diameter, and u

Formulations Model problem Strong Formulation Find u such that Vu=f in n2 a =0 on I for a polygonal domain

Finite Difference Problem Definition Formulas

Dirichlet Model Problems Strong Form Domain: Q =(0, 1) Find u such that (0)=(1)=0 for given f SMA-HPO⊙1999M Poisson in Rl. Formulation 1

A posteriori error estimates are arguably more useful than a priori esti mates since we know uh. Bear in mind, however, that (i) in most methods

Finite Volume Computational Cells Discretization

Motivation The Poisson problem has a strong formulation; a minimization formulation; and a weak formulation. The minimization/weak formulations are more general than the strong formulation in terms of reqularity and admissible data

1.1 最优化问题简介 1.2 最优化方法概述

信赖域方法是求解最优化问题的另一类有效 方法．其最初的设计思想可追溯至Levenberg Marquart 和 对Gauss－Newton法的修 正．线搜索方法是把一个复杂的最优化问题转化 成一系列简单的一维寻优问题．信赖域方法是把 最优化问题转化为一系列相对简单的局部寻优 问题．

Scalar Definitions Conservation Laws