Dual System Least-Squares Finite Element Method for a Hyperbolic Problem

Eunjung Lee, Hyesun Na

Research output: Contribution to journalArticlepeer-review

Abstract

This study investigates the dual system least-squares finite element method, namely the LL method, for a hyperbolic problem. It mainly considers nonlinear hyperbolic conservation laws and proposes a combination of the LL method and Newton's iterative method. In addition, the inclusion of a stabilizing term in the discrete LL minimization problem is proposed, which has not been investigated previously. The proposed approach is validated using the one-dimensional Burgers equation, and the numerical results show that this approach is effective in capturing shocks and provides approximations with reduced oscillations in the presence of shocks.

Original languageEnglish
JournalComputational Methods in Applied Mathematics
DOIs
Publication statusAccepted/In press - 2021

Bibliographical note

Publisher Copyright:
© 2021 Walter de Gruyter GmbH, Berlin/Boston 2021.

All Science Journal Classification (ASJC) codes

  • Numerical Analysis
  • Computational Mathematics
  • Applied Mathematics

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