This paper is concerned with the development of weak Galerkin (WG) finite element method for optimal control problems governed by second order elliptic partial differential equations (PDEs). It is advantageous to use discontinuous finite elements over the traditional $C^1$ finite elements here. Optimal order error estimates are established and confirmed by some numerical tests.

翻译：本文研究二阶椭圆型偏微分方程（PDEs）最优控制问题的弱Galerkin（WG）有限元方法。在此类问题中，使用间断有限元相较于传统的$C^1$连续有限元具有明显优势。本文建立了最优阶误差估计，并通过数值试验验证了其有效性。