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 H 1 + s ( Ω ) with s ∈ ( 0 , 1 2 ) . Furthermore, a robust convergence is proved even if the solution is exactly in H 1 ( Ω ) .