In this paper, we propose a weak Galerkin finite element method (WG) for solving singularly perturbed convection-diffusion problems on a Bakhvalov-type mesh in 2D. Our method is flexible and allows the use of discontinuous approximation functions on the meshe. An error estimate is devised in a suitable norm and the optimal convergence order is obtained. Finally, numerical experiments are given to support the theory and to show the efficiency of the proposed method.

翻译：本文针对二维Bakhvalov型网格上的奇异摄动对流扩散问题，提出了一种弱Galerkin有限元方法（WG）。该方法具有灵活性，允许在网格上使用间断逼近函数。我们在适当的范数下推导了误差估计，并获得了最优收敛阶。最后通过数值实验验证了理论结果，并证明了所提方法的有效性。