We formulate and analyze a goal-oriented adaptive finite element method (GOAFEM) for a semilinear elliptic PDE and a linear goal functional. The strategy involves the finite element solution of a linearized dual problem, where the linearization is part of the adaptive strategy. Linear convergence and optimal algebraic convergence rates are shown.

翻译：我们为半线性椭圆形PDE和线性目标功能制定并分析一种面向目标的适应性有限要素方法(GOAFEM),该战略涉及线性双重问题的有限要素解决办法,即线性线性是适应性战略的一部分,显示线性趋同率和最佳代数趋同率。