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The paper presents error estimates within a unified abstract framework forthe analysis of FEM for boundary value problems with lineardiffusion-convection-reaction equations and boundary conditions of mixed type.Since neither conformity nor consistency properties are assumed, the method iscalled completely discrete. We investigate two different stabilizeddiscretizations and obtain stability and optimal error estimates in energy-typenorms and, by generalizing the Aubin-Nitsche technique, optimal error estimatesin weaker norms.

Error estimates for completely discrete FEM in energy-type and weaker norms