A new and simple implementation of the element-local L2-projected continuous finite element method

In this paper we present a new and simple method, modified from the original element-local L2-projected continuous finite element method, to resolve some static electromagnetic problems in two dimension. This numerical method is established on the least-square process to minimize the total error’s energy, where the residual due to an additional element-local projection is considered. Many numerical experiments are presented for the electrostatic problem, the Maxwell’s equations and the Maxwell’s eigenvalue problem, and the numerical performances are excellent with the optimal convergence orders even for the non-H1 solution.