Finite Element Triangulation Discretization ∪Tn N3 Th∈Th TR: elements k=1 K ai:nodes, interior 1 n boundary SMA-HPO⊙1999M FEM Poisson in R 5
Finite Element Approximation Discretization Space(Linear Elements) Xn={∈x|vn∈P1(T),VTn∈Th} 0 U∈C0() P1(Th):0n=c0+、C+、cyy,c,cmyy∈ SMA-HPO⊙1999M FEM Poisson in R 6
Finite Element Approximation Discretization Basis(Nodal) h=span{1,…,9n} 9;∈Xh,(m;)=6,1≤i,j≤m Support of p ppi nonzero SMA-HPO⊙1999M FEM Poisson in R2 7
Finite Element Approximation Discretization Basis(Nodal) Nodal interpretation: v E Xh 0=∑ vi pila)i 0(a )=∑091(m)=∑016n→=0(m =1 SMA-HPO⊙1999M FEM Poisson in R 8
Finite Element “ Projection Discretization Rayleigh-Ritz or Galerkin Rayleigh-Ritz Wh= arg min ba(o, w)-e(o) D∈Xh J(w) Galerkin: Uh E X, satisfies a(uh,v)=e(v),Vv∈Xh SMA-HPO⊙1999M FEM Poisson in R 9