麻省理工学院：《偏微分方程式数字方法》（英文版）Lecture 13 Finite Element Methods for Elliptic Problems

The Dirichlet Minimization Principle Problem Proof 1 J(x+)=J(u)+ Vu.VdA,V∈X 2 >0 unless 0= 0 J(u)>J(u),V0∈X,w≠t a is the minimizer of (w) E1 SMA-HPO⊙1999M Variational Formulation 10

The Dirichlet Weak Formulation Problem Statement Find a∈ X such that 6J()=0,V0∈X Vu. VO dA f vdA Vu∈X see Slide 9 for proof SMA-HPO⊙1999M Variational Formulation 11

The Dirichlet Weak Formulation Problem Definitions Linear space. Y A set Y is a linear(or vector) space if V1,2∈Y,1+2∈Y Va∈i,Vw∈Y,a0∈Y SMA-HPO⊙1999M Variational Formulation 12