We consider the goal-oriented error estimates for a linearized iterative solver for nonlinear partial differential equations. For the adjoint problem and iterative solver we consider, instead of the differentiation of the primal problem, a suitable linearization which guarantees the adjoint consistency of the numerical scheme. We derive error estimates and develop an efficient adaptive algorithm which balances the errors arising from the discretization and use of iterative solvers. Several numerical examples demonstrate the efficiency of this algorithm.

翻译：我们考虑对非线性部分差异方程式的线性迭代求解器进行面向目标的误差估计。对于连接问题和迭代求解器,我们考虑的不是区分原始问题,而是适当的线性化,这保证了数字方法的共性一致性。我们得出误差估计,并开发一种高效的适应算法,平衡因迭代求解器的离散和使用而产生的误差。几个数字例子证明了这一算法的效率。