Discretization of the Poisson Problem in RI: Theory and Implementation Apr|7&9,2003
Goals Theory A priori A priori error estimates N1 bound various“ measures” of u exact]-un [approximate] in terms of C(n, problem parameters h [mesh diameter, and u SMA-HPO⊙1999M Poisson in IR: Theory Practice 1
Goals Theory A priori uL2xn=f,(0)=(1)=0 a(u,)=e(u) V∈X (00。0)三 Wr Ur da, e(o)=f 0 a 0 X={0∈H(92)|(0)=0(1)=0} SMA-HPO⊙1999M Poisson in IR: Theory Practice 2
Goals Theory A priori Up a(uh,)=e(u),V0∈Xh (00。0)三 Wr Vr da, e(o)=f 0 a 0 Xh={v∈Xvl2∈m1(T),VTh∈Th} SMA-HPO⊙1999M Poisson in IR: Theory Practice 3
Goals Theory A posteriori A posteriori error estimates N2 bound various“ measures” of a [exact]-uh [approximate in terms of C(Q, problem parameters h[mesh diameter], and uh SMA-HPO⊙1999M Poisson in IR: Theory Practice 4