A new a priori error analysis of nonconforming and mixed finite element methods

In this short paper, we derive an a priori error analysis for the lowest order nonconforming and mixed finite element discretizations of the second order equation with low-regularity exact solutions only, belonging to H1+s(Ω)H1+s(Ω) with s∈(0,12). Furthermore, a robust convergence is proved even if the solution is exactly in H1(Ω)H1(Ω).