FEM for the Poisson Problem in R2 Apri14&16,2003
Formulations Model problem Strong Formulation Find u such that Vu=f in n2 a =0 on I for a polygonal domain N1 SMA-HPO⊙1999M FEM Poisson in R 1
Formulations Model problem Minimization/Weak Formulations Find u= arg min da(w, w)-e(w); ∈X J(w) or find∈ X such that a(u,0)=(),v∈X SMA-HPO⊙1999M FEM Poisson in R 2
Formulations Model problem Minimization/Weak Formulations where X={v∈H(s)|vr=0}=H(9), C(0U。0 Vw. VU dA SPD 0 f vdA bounded SMA-HPO⊙1999M FEM Poisson in R 3
Regularity Model problem In general, ullH1(o)< ClellH-1(0) If f EL (S)and n is convex, ur2()≤Cf(g) N2 important for convergence rate SMA-HPO⊙1999M FEM Poisson in R 4