The post-processing of the solution of variational problems discretized with Galerkin finite element methods is particularly useful for the computation of quantities of interest. Such quantities are generally expressed as linear functionals of the solution and the error of their approximation is bounded by the error of the solution itself. Several a posteriori recovery procedures have been developed over the years to improve the accuracy of post-processed results. Nonetheless such recovery methods usually deteriorate the convergence properties of linear functionals of the solution and, as a consequence, of the quantities of interest as well. The paper develops an enhanced gradient recovery scheme able to both preserve the good qualities of the recovered gradient and increase the accuracy and the convergence rates of linear functionals of the solution.

中文翻译：

---

超收敛线性泛函的正交约束梯度重建

使用 Galerkin 有限元方法离散化的变分问题解的后处理对于计算感兴趣的量特别有用。这些量通常表示为解的线性函数，它们的近似误差受解本身的误差限制。多年来已经开发了几种后验恢复程序，以提高后处理结果的准确性。尽管如此，这种恢复方法通常会恶化解的线性泛函的收敛特性，因此也会恶化感兴趣的数量。