Richardson extrapolation is applied to a simple first-order upwind difference scheme for the approximation of solutions of singularly perturbed convection-diffusion problems in one dimension. Robust a posteriori error bounds are derived for the proposed method on arbitrary meshes. It is shown that the resulting error estimator can be used to stear an adaptive mesh algorithm that generates meshes resolving layers and singularities. Numerical results are presented that illustrate the theoretical findings.

翻译：将Richardson外推应用于简单的一阶迎风差分格式，以逼近一维奇异摄动对流扩散问题的解。针对所提出的方法，在任意网格上推导了稳健的后验误差界。结果表明，所得误差估计量可用于引导自适应网格算法，从而生成能够解析层与奇异性的网格。文中给出了数值结果以验证理论发现。