Least-square finite element method for electromagnetic fields in 2-D

摘要

A least-squares finite element approximation scheme for electromagnetic fields in two-dimensional domains is discussed. Considering the magnetic-field strength \lsH\ls and the vector of the current density \lsJ̃\ls as unknowns, we describe Maxwell's equation as a time-dependent form in three dimensions, then reduce it into two-dimensional steady problems of two categories. Based on the first-order system of partial differential equations, the least-squares method is applied to the finite-element method. The rates of convergence for both \lsH\ls and \lsJ̃\ls achieve optimal order. This method creates an easy way to develop computer software.