The proper generalized decomposition is a well‐established reduced order method, used to efficiently obtain approximate solutions of multi‐dimensional problems in a procedure that controls the effects of the “curse of dimensionality.” The question of assessing the quality of the solutions obtained and adapting the approximations assumed, for example, the finite element meshes used, so that the best result is obtained at minimal cost, remains a relevant challenge. This article deals with finite element solutions for solid mechanics problems, using the error obtained from a dual analysis, the difference between complementary solutions, to bound the error in the solutions and to drive an optimal adaptivity process, which obtains meshes with errors significantly lower than those obtained using a uniform refinement.

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适当的广义分解解的误差估计：双重方法

适当的广义分解是一种行之有效的降阶方法，用于控制控制“维数诅咒”的过程中的多维问题的有效解。评估获得的解决方案的质量并调整所假定的近似值（例如使用的有限元网格）以便以最小的成本获得最佳结果的问题仍然是一个挑战。本文针对固体力学问题的有限元解决方案，利用从双重分析中获得的误差，互补解之间的差异，限制解中的误差并驱动最优的适应性过程，从而获得误差明显低于使用均匀精修获得的结果。