Nonconforming quadrilateral EQ1rot finite element method for Ginzburg-Landau equation

Nonconforming finite element method is studied for a linearized backward fully-discrete scheme of the Ginzburg-Landau equation with the quadrilateral EQ1rot element. The unconditional convergent result of order O(h + tau) in the broken H-1-norm is deduced rigorously based on a splitting technique, by which the ratio between the subdivision parameter h and the time step tau is removed. Furthermore, numerical results are provided to confirm the theoretical analysis. The analysis developed herein can be regarded as a framework to deal with the unconditional convergent analysis of the Ginzburg-Landau equation for other known low order nonconforming elements.