The Interpolant Theory Approximation Theory fw∈x, and wlTy∈C2(mh),VTh∈Th,then -mlm(a)≤bmax( max w Th∈Th -1hL2() <h2 max max lw' Th∈Th SMA-HPO⊙1999M Poisson in R: Theory Practice 10
The Interpolant Theory Approximation Theory. Sketch of proof (-x)r k 九 九 k k SMA-HPO⊙1999M Poisson in R: Theory Practice 11
The Interpolant Theory Approximation Theory. (0-)rk( w-Lhw)Tk n ac h h max w ∈ K w-Ihw)k dc hh max max w 九 k=l.K c∈m k=1 E2 SMA-HPO⊙1999M Poisson in R: Theory Practice 12
The Interpolant Theory Approximation Theory fv∈X,andw∈H2(3,Th), w-Ir hulL(n) T 0112(2,Th) h2 0U-ThU2()-丌 ur2a,万) where K K 00 H2(32,Th) ∑1cn=∑/2+02+0dm k=1 k=1h SMA-HPO⊙1999M Poisson in R: Theory &Practice13
Error: Energy Norm Theory Definition Define the energy, or "a", norm a as l|2=a(v,) generally ly) da 0 (here) Note: is problem-dependent SMA-HPO⊙1999M Poisson in R: Theory Practice 14