A finite volume method based on the Crouzeix–Raviart element for elliptic PDE's in two dimensions

Abstract. We introduce and analyse a finite volume method for the discretization of elliptic boundary value problems in $\mathbb{R}^2$. The method is based on nonuniform triangulations with piecewise linear nonconforming spaces. We prove optimal order error estimates in the $L^2$–norm and a mesh dependent $H^1$–norm.

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