Numerical Analysis for Conservation Laws Using l1 Minimization

Anne Gelb, X. Hou, Q. Li

Research output: Contribution to journalArticle

Abstract

This paper develops and analyzes a new numerical scheme for solving hyperbolic conservation laws that combines the Lax Wendroff method with l1 regularization. While prior investigations constructed similar algorithms, the method developed here adds a new critical conservation constraint. We demonstrate that the resulting method is equivalent to the well known lasso problem, guaranteeing both existence and uniqueness of the numerical solution. We further prove consistency, convergence, and conservation of our scheme, and also show that it is TVD and satisfies the weak entropy condition for conservation laws. Numerical solutions to Burgers’ and Euler’s equation validate our analytical results.

Original languageEnglish (US)
JournalJournal of Scientific Computing
DOIs
StatePublished - Jan 1 2019
Externally publishedYes

Keywords

  • Conservation laws
  • l regularization
  • Polynomial annihilation

ASJC Scopus subject areas

  • Software
  • Theoretical Computer Science
  • Numerical Analysis
  • Engineering(all)
  • Computational Theory and Mathematics
  • Computational Mathematics
  • Applied Mathematics

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