An <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" id="d1e6237" altimg="si505.svg"><mml:msup><mml:mrow><mml:mi>L</mml:mi></mml:mrow><mml:mrow><mml:mi>p</mml:mi></mml:mrow></mml:msup></mml:math>- primal–dual weak Galerkin method for convection–diffusion equations

In this article, the authors present a new Lp-primal–dual weak Galerkin method (Lp-PDWG) for convection–diffusion equations. Comparing with standard L2-PDWG method, solution calculated from Lp-PDWG may exhibit some important advantages and features (e.g., less jumps cross element interface when p?1, or sparsity by using p=1 wavelet basis approximation). The existence uniqueness of numerical is discussed, an optimal-order error estimate derived in Lq-norm primal variable, where 1p+1q=1 p>1. Furthermore, estimates are established approximation dual variable Wm,p norm, 0?m?2. Numerical results presented to demonstrate efficiency accuracy proposed method.