In this work, we apply multi-goal oriented error estimation to the finite element method. In particular, we use the dual weighted residual method and apply it to a model problem. This model problem consist of locally different coercive partial differential equations in a checkerboard pattern, where the solution is continuous across the interface. In addition to the error estimation, the error can be localized using a partition of unity technique. The resulting adaptive algorithm is substantiated with a numerical example.

翻译：本文工作中，我们将多目标导向的误差估计方法应用于有限元法。具体而言，我们采用对偶加权残差法，并将其应用于一个模型问题。该模型问题由局部不同的强制性偏微分方程以棋盘格模式构成，其解在交界面处保持连续。除误差估计外，通过单位分解技术可实现误差的局部化。最终构建的自适应算法通过数值算例进行了验证。