Nonconforming FEMs For Nolinear Problems

With the continuous development of modern science and technology,engineering calculation has grow more and more fast than before.Differential equation plays an important role in engineering calculation.So it's valuable to study numerical solution of differential equations.And Finite Elements Method is one of the common methods for this.This paper focus on p-Laplace Problems,which lead to a degenerate con-vex minimization problem.We use the discrete Raviart-Thomas mixed finite element method(dRT-MFEM)to solve this problem at the first time.According to the anal-ysis,we introduce a quasi-norm,establish its equivalence with the Crouzeix-Raviart nonconforming finite element method(CR-NCFEM).The sharper quasi-norm a priori and a posteriori error estimates of this two methods are presented.At last,numerical experiments are provided to verify the analysis.