A Mixed Discontinuous Galerkin Method Without Interior Penalty for Time-Dependent Fourth Order Problems

@article{Liu2018AMD,
  title={A Mixed Discontinuous Galerkin Method Without Interior Penalty for Time-Dependent Fourth Order Problems},
  author={Hailiang Liu and Peimeng Yin},
  journal={Journal of Scientific Computing},
  year={2018},
  volume={77},
  pages={467-501}
}
A novel discontinuous Galerkin (DG) method is developed to solve time-dependent bi-harmonic type equations involving fourth derivatives in one and multiple space dimensions. We present the spatial DG discretization based on a mixed formulation and central interface numerical fluxes so that the resulting semi-discrete schemes are $$L^2$$L2 stable even without interior penalty. For time discretization, we use Crank–Nicolson so that the resulting scheme is unconditionally stable and second order… Expand
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