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.
}, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/9041.html} }