3.3 Galerkin's Method

If the weighting functions $W_i$ are chosen to be the same as those applied in the sum of the approximation ( $W_i(\vec{r}) = N_i(\vec{r})$ ), the weighted residual method merges into Galerkin's method. If $\mathcal{L}$ is self-adjoint, the matrix from (3.12) is symmetric and Galerkin's method leads to the same linear equation system as those given by the Ritz method [38].