An Lp- primal-dual weak Galerkin method for convection-diffusion equations
An Lp- primal-dual weak Galerkin method for convection-diffusion equations
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DOI：
10.1016/j.cam.2022.114698
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发表时间：
2022-08
影响因子：
2.4
通讯作者：
Waixiang Cao;Chunmei Wang;Junping Wang
中科院分区：
文献类型：
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作者：
Waixiang Cao;Chunmei Wang;Junping Wang
本文提出了求解对流扩散方程的一种新的L p-原始-对偶弱Galerkin方法(L p-PDWG)。与标准的L 2-→方法相比，由L p-PDWG计算的解可能显示出一些重要的优点和特点(例如，当p-PDWG为1时，跨越单元界面的跳跃较少，或者利用p=1和小波基近似的稀疏性)。讨论了数值解的存在唯一性，得到了原变量在L q范数下的最优阶误差估计，其中1 p+1q=1且p>；1.进而建立了对偶变量在标准Wm，p范数，0≤m≤2下数值逼近的误差估计.数值结果表明了所提出的L p-PDWG方法的有效性和准确性.
In this article, the authors present a new L p-primal–dual weak Galerkin method (L p-PDWG) for convection–diffusion equations. Comparing with the standard L 2-PDWG method, the solution calculated from the L p-PDWG may exhibit some important advantages and features (eg, less jumps cross the element interface when p→ 1, or sparsity by using p= 1 and wavelet basis approximation). 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 1 p+ 1 q= 1 with p> 1. Furthermore, error estimates are established for the numerical approximation of the dual variable in the standard W m, p norm, 0≤ m≤ 2. Numerical results are presented to demonstrate the efficiency and accuracy of the proposed L p-PDWG method.