An L^p-primal-dual finite element method for first-order transport problems

2022/12/24 by Dan Li, Li, Dan, Chunmei Wang +3 · 2 citations
Mathematics · Engineering · #Differential Equations and Numerical Methods #Differential Equations and Boundary Problems #Advanced Numerical Methods in Computational Mathematics

paper · pdf · doi:10.48550/arxiv.2212.12783

Abstract

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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