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

翻译：本文在一个统一的抽象框架内，针对具有线性扩散-对流-反应方程及混合型边界条件的边值问题，提出了有限元法（FEM）的误差估计。由于未假设任何协调性或一致性性质，该方法被称为完全离散方法。我们研究了两种不同的稳定化离散格式，在能量型范数下获得了稳定性和最优误差估计；同时，通过推广Aubin-Nitsche技巧，在较弱范数下也得到了最优误差估计。