2nd Kind Discretization Galerkin Make Residual orthogonal to basis piley(e)dac (x) ∑ pi() dac +/p:(a)2On;G(e, e) (ae)da dat Note: Pi is the support of pi(a) SMA-HPC⊙2003MT First and Second Kind 5
2nd Kind Discretization Galerkin Cont Assume Orthonormal Basis Orthogonality 9(x)93(c)da=0 Normalization Pila)pile)da=1 SMA-HPC⊙2003MT First and Second Kind 6
2nd Kind Discretization Comparison Collocation Galerkin with one point quadrature One point quadrature implies g(x)y(x)da≈yp()(x) Ci= quadrature point Wi= quadrature weight SMA-HPC⊙2003MT First and Second Kind 7
2nd Kind Discretization Comparison Cont One point quadrature implies 9(a)∑on9()d≈(;)∑an 1 2y(c2) ∑ G(i, a)ei (a )dac SMA-HPC⊙2003MT First and Second Kind 8