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.
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© 2021 Walter de Gruyter GmbH, Berlin/Boston 2022.
All Science Journal Classification (ASJC) codes
- Numerical Analysis
- Computational Mathematics
- Applied Mathematics