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arXiv · 2111.11005

An $L^p$- Primal-Dual Weak Galerkin Method for Convection-Diffusion Equations

Waixiang Cao·Chunmei Wang·Junping Wang
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Abstract

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.

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Waixiang Cao, Chunmei Wang, Junping Wang. 2021-11-22. An $L^p$- Primal-Dual Weak Galerkin Method for Convection-Diffusion Equations. https://arxiv.org/abs/2111.11005

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