The Lumped Mass Nonconforming Finite Element Analysis For Two Classes Of Nonlinear Equations

In this paper,firstly,a low order Crouzeix-Raviart type anisotropic nonconforming triangular element is applied to the nonstationary Navier-Stokes equations.The approximation scheme of a lumped mass nonconforming finite element methods for the problem is proposed.The error estimates are derived both in the L~2 norm and enery norm for the velocity and the L~2 norm for the pressure on anisotropic meshes by introducing auxiliary finite element spaces technique.Secondly,the lumped mass nonconforming finite element approximation scheme is proposed to a kind of nonlinear parabolic integro-differential equations.The L~2 norm error estimate is derived on anisotropic meshes without referring to the traditional nonclassical elliptic projection.