Discretization of the Poisson Problem in rl Formulation Apri2,2003
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
Dirichlet Model Problems Minimization Statement Define X≡Hb(2) Find u= arg min J(w) U∈X where au dr a ac 2 0 SMA-HPO⊙1999M Poisson in Rl. Formulation 2
Dirichlet Model Problems Weak Formulation Find u∈ X such that 6J(u)=0,V0∈X E U ai fdm,u∈X 0 SMA-HPO⊙1999M Poisson in Rl. Formulation 3
Dirichlet Model Problems Notation Define a(00,0 UmUr d 0 e(o v d Minimization: u=arg min a(w, w)e(w) ∈X Weak u∈X:a(u,)=e(v),Vv∈X SMA-HPO⊙1999M Poisson in Rl. Formulation 4