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:<math>\quad (3) \qquad \qquad \forall v \in X_{D,0},\qquad \int_{\Omega} \nabla_D u(x)\cdot\nabla_D v(x) dx = \int_{\Omega} f(x)\Pi_D v(x) dx. </math>
The GDM is then in this case a nonconforming method for the approximation of (2), which includes the nonconforming finite element method. Note that the reciprocal is not true, in the sense that the GDM framework includes methods such that the function <math>\nabla_D u</math> cannot be computed from the function <math>\Pi_D u</math>.
Then the following error estimate, inspired by [Strang,1972], holds
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\left|\int_\Omega \left(\nabla_D v(x)\cdot\varphi(x) + \Pi_D v(x) \operatorname{div}\varphi(x)\right) \, dx \right|}{\Vert \nabla_D v \Vert_{L^2(\Omega)^d}}, </math>
which measures the defect of conformity.
Note that (4) and (5) are implied by [[Céa's lemma]] in the case of a conforming approximation (in the sense that the operators <math>\Pi_D</math> and <math>\nabla_D</math> are such that, for all <math>v\in X_{D,0}</math>, <math>\Pi_D v \in H^1_0(\Omega)</math> and <math>\nabla_D v = \nabla(\Pi_D v)</math>, and then <math>C_D</math> is replaced by the Poincaré constant, leading to a Galerkin method as described below).
Then the core properties which are sufficient for the convergence of the method are, for a family of GDs, the coercivity, the GD-consistency and the limit-conformity properties, as defined in the next section. These three core properties are sufficient to prove the convergence of the GDM for linear problems. For nonlinear problems (nonlinear diffusion, degenerate parabolic problems...), we add in the next section two other core properties which may be required.
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