An L^p- Primal-Dual Weak Galerkin Method for Convection-Diffusion Equations
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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 1/p+1/q=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.
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