An Lp- primal-dual weak Galerkin method for convection-diffusion equations

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 (e.g., 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,W-p norm, 0 <= m <= 2. Numerical results are presented to demonstrate the efficiency and accuracy of the proposed L-p-PDWG method. (C) 2022 Elsevier B.V. All rights reserved.