Explicit error bounds for a nonconforming finite element method

Let u be the solution of the following model: { find   u ∈ H 0 1 ( Ω )   such   that − Δ u = f   in   Ω , https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780203756034/6b58283d-8100-4221-bafc-5f6bf7d0c46b/content/eq629.tif"/>

where f is a given function in L ²(Ω) and Ω a bounded set in ℝ² with a polygonal boundary. Let u^h be a finite element approximation of u. The goal of this paper is to suggest an explicit bound of the error (u − u^h ). Furthermore this bound is obtained without complex computations. The basic idea is to define locally an admissible vector field for the dual model.