A new Lp-primal-dual weak Galerkin method (Lp-PDWG) with p>1 is
proposed for the first-order transport problems. The existence and uniqueness
of the Lp-PDWG numerical solutions is established. In addition, the
Lp-PDWG method offers a numerical solution which retains mass conservation
locally on each element. An optimal order error estimate is established for the
primal variable. A series of numerical results are presented to verify the
efficiency and accuracy of the proposed Lp-PDWG scheme.Comment: 26 pages, 7 figures, 10 tables. arXiv admin note: text overlap with
arXiv:1906.0733