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.
Bibliographical notePublisher Copyright:
© 2021 Walter de Gruyter GmbH, Berlin/Boston 2021.
All Science Journal Classification (ASJC) codes
- Numerical Analysis
- Computational Mathematics
- Applied Mathematics