An L^p-primal-dual finite element method for first-order transport problems
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A new L^p-primal-dual weak Galerkin method (L^p-PDWG) with p>1 is proposed for the first-order transport problems. The existence and uniqueness of the L^p-PDWG numerical solutions is established. In addition, the L^p-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 L^p-PDWG scheme.
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