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.
Funding source: National Research Foundation of Korea
Award Identifier / Grant number: 2015R1D1A1A01056909
Award Identifier / Grant number: 2018R1D1A1B07042973
Funding statement: This work was supported by the Basic Science Research Program through the NRF of Korea, 2015R1D1A1A01056909 and 2018R1D1A1B07042973.
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