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

Dan Li; Chunmei Wang; Junping Wang

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

Numerical Analysis 2022-12-27 v1 Numerical Analysis

Authors: Dan Li , Chunmei Wang , Junping Wang

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.

Keywords

weak galerkin finite element methods optimal transport traveling salesman problem

Cite

@article{arxiv.2212.12783,
  title  = {An $L^p$-primal-dual finite element method for first-order transport problems},
  author = {Dan Li and Chunmei Wang and Junping Wang},
  journal= {arXiv preprint arXiv:2212.12783},
  year   = {2022}
}

Comments

26 pages, 7 figures, 10 tables. arXiv admin note: text overlap with arXiv:1906.07336

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