In this article, the authors present a new $L^p$- primal-dual weak Galerkin method ($L^p$-PDWG) for convection-diffusion equations with $p>1$. The existence and uniqueness of the numerical solution is discussed, and an optimal-order error estimate is derived in the $L^q$-norm for the primal variable, where $\frac 1p+\frac 1q=1$. Furthermore, error estimates are established for the numerical approximation of the dual variable in the standard $W^{m,p}$ norm, $0\le m\le 2$. Numerical results are presented to demonstrate the efficiency and accuracy of the proposed $L^p$-PDWG method.

翻译：在本条中,作者提出了一种新的用$p$-纯度弱的Galerkin法(L$P$-PDWG),用于以$p>1美元对流-扩散方程式。讨论了数字解决方案的存在和独特性,并用$q$-norm得出了最优顺序错误估计值,原始变量为$\frac 1p ⁇ frac 1q=1美元。此外,为标准$W ⁇ m,p}规范中的双变量数字近似值确定了错误估计值,0\le m\le 2美元。数字结果显示拟议的$L$-PDWG方法的效率和准确性。