Istituto di Matematica Applicata e Tecnologie Informatiche     
Cornetti G. M. A mixed discontinuous finite element method for diffusion problems. Technical report ercim.cnr.ian//1998-1088, 1998.
A finite element method for solving diffusion problems, which makes use of a discrete functional space that allows interelement discontinuities, is proposed. The method is derived by rewriting the diffusion equation as a first order system and by introducing the gradient of the solution as an auxiliary variable. Piecewise linear and piecewise constant discontinuous finite elements are employed for the solution and for its gradient respectively. The method is proved to converge to the exact solution with optimal convergence rate, and some numerical results are given to support the theoretical analysis. Since the main interest of the method is to solve the diffusion part of convection-diffusion systems in the convection dominated regime, the discretization of a linear convection-diffusion problem is discussed in the appendix.
Subject Discontinuous Galerkin method, Mixed finite elements, Second-order elliptic problems, Convection-diffusion equation

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