A Discontinuous Galerkin Method for the Intrinsic Beam Model with Kelvin-Voigt Damping

@misc{sundriyal2026discontinuous,
  title = {{A Discontinuous Galerkin Method for the Intrinsic Beam Model with Kelvin-Voigt Damping}},
  author = {Shivam Sundriyal and Christian Bleffert and Lukas Dreyer and Melven Röhrig-Zöllner and Gregor Gassner and Vadym Aizinger},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.08397},
  eprint = {2609.08397},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.08397},
}

TY  - UNPB
TI  - A Discontinuous Galerkin Method for the Intrinsic Beam Model with Kelvin-Voigt Damping
AU  - Shivam Sundriyal
AU  - Christian Bleffert
AU  - Lukas Dreyer
AU  - Melven Röhrig-Zöllner
AU  - Gregor Gassner
AU  - Vadym Aizinger
PY  - 2026
DA  - 2026/09/08
PB  - arXiv
DO  - 10.48550/arxiv.2609.08397
UR  - https://arxiv.org/abs/2609.08397
AB  - We present an energy-stable discontinuous Galerkin (DG) spatial discretization of the intrinsic beam equations with Kelvin-Voigt damping. We reformulate the governing equations by splitting the total sectional resultants into elastic and viscous parts, thereby exposing a mixed system without mixed space-time derivatives. For homogeneous cantilever boundary data, the continuous system obeys an energy dissipation identity. With characteristic upwinding and alternating auxiliary traces the DG discretization is energy stable at the semidiscrete level for the stated homogeneous split boundary closure. The method is implemented in the Julia-based simulation framework Trixi.jl. A physically compatible manufactured solution with all state and viscous components active assesses convergence, while a rotating-beam test verifies the analytic constant-spin branch and the actuated energy balance.
ER  -