This article devises a new primal-dual weak Galerkin finite element method for the convection-diffusion equation. Optimal order error estimates are established for the primal-dual weak Galerkin approximations in various discrete norms and the standard $L^2$ norms. A series of numerical experiments are conducted and reported to verify the theoretical findings.

中文翻译：

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对流扩散问题的新原始对偶弱伽辽金有限元方法

本文针对对流-扩散方程设计了一种新的原始-对偶弱Galerkin有限元方法。为各种离散范数和标准 $L^2$ 范数中的原始-对偶弱伽辽金近似建立了最优阶误差估计。进行并报告了一系列数值实验以验证理论发现。