Error in projection of planewaves using various basis functions

In this paper, the projection error of RMS in 1D and 2D case is analyzed. The analytical projection error on the infinite meshes are given in closed form for the pulse basis, triangular basis, the second-order basis in 1D case, the divergence-conforming basis on rectangular element and the one-directional triangular element in 2D case. In addition, the projection error is numerically calculated for various basis functions with a finite computational domain. There are good agreements between the analytical and numerical results. It is found the projection error of p-th order 1D basis function is asymptotically proportional to (p+1) power of the size of the element. More results and discussions about the projection errors will be presented at the conference.