A primal-dual approach for solving conservation laws with implicit in time approximations

  title={A primal-dual approach for solving conservation laws with implicit in time approximations},
  author={Siting Liu and Stanley J. Osher and Wuchen Li and Chi-Wang Shu},
  journal={J. Comput. Phys.},
. In this work, we propose a novel framework for the numerical solution of time-dependent conservation laws with implicit schemes via primal-dual hybrid gradient methods. We solve an initial value problem (IVP) for the partial differential equation (PDE) by casting it as a saddle point of a min-max problem and using iterative optimization methods to find the saddle point. Our approach is flexible with the choice of both time and spatial discretization schemes. It benefits from the implicit… 
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