Neumann” Model Problems Notation Define a(w, v)=/wr Ur dac 0 e(u f v dc+9v(1) N2 0 Minimization: u= arg min a(w, w)-e(w u∈X2 Weak u∈X:a(u,)=e(v),Vv∈X SMA-HPO⊙1999M Poisson in IR. Formulation 10
Rayleigh-Ritz Approximation Approach Mesh a=0 a=1 0 k i an+ K 3=∪mT,k=1,…,K=7+1:emen k=1 c2,=0,,,,+1: nodes N3 SMA-HPO⊙1999M Poisson in IR. Formulation 11
Rayleigh-Ritz Approximation Approach space Xh X h={∈X{rk∈P1(①h),k=1,……,K U∈Xh piecewise linear 0(0)=0 0 0 v continuous N4 SMA-HPO⊙1999M Poisson in IR. Formulation 12
Rayleigh-Ritz Approximation Approach Basis General definition: given a linear space Y, a set of members y;∈Y,j=1,…,M is a basis for Y if and only if Vy∈Y,彐 unique C;∈ IR such that M y dim(ension)(Y)=M N5 N6 E1 E2 SMA-HPO⊙1999M Poisson in R: Formulation 13