The L2-Norm Error Estimate of Nonconforming Finite Element Method for the 2nd Order Elliptic Problem with the Lowest Regularity

Abstract

The abstract $L^2$-norm error estimate of nonconforming finite element method is established. The uniformly $L^2$-norm error estimate is obtained for the nonconforming finite element method for the second order elliptic problem with the lowest regularity, i.e., in the case that the solution $u∈H^1(Ω)$ only. It is also shown that the $L^2$-norm error bound we obtained is one order higher than the energe-norm error bound.