A second-order nonconforming rectangular finite element method for approximating Maxwell's equations
The main objective of this paper is to present a new rectangular nonconforming finite element scheme with the second-order convergence behavior for the approximation of Maxwell's equations. Then the corresponding optimal error estimates are derived. The difficulty in the construction of this finite element scheme is how to choose a compatible pair of degrees of freedom and shape function space so as to make the consistency error due to the nonconformity of the element being of order \(O(h^3)\), properly one order higher than that of its interpolation error \(O(h^2)\) in the broken energy norm, where \(h\) is the subdivision parameter tending to zero.
scientific article; zbMATH DE number 6145664
scientific article