Structure preserving approximation of dissipative evolution problems

Authors

Abstract

We present a framework for the systematic numerical approximation of nonlinear evolution problems with dissipation. The approach is based on rewriting the problem in a canonical form that complies with the underlying energy-dissipation structure. We show that the corresponding weak formulation then allows for a dissipation-preserving approximation by Galerkin methods in space and discontinuous Galerkin methods in time. The proposed methodology is rather general and can be applied to a wide range of applications. This is demonstrated by discussion of some typical examples ranging from diffusive partial differential equations to dissipative Hamiltonian systems.

Keywords

37K05; 37L65; 47J35; 65J08

Citation

Journal: Numerische Mathematik
Year: 2019
Volume: 143
Issue: 1
Pages: 85–106
Publisher: Springer Science and Business Media LLC
DOI: 10.1007/s00211-019-01050-w

BibTeX

@article{Egger_2019,
  title={{Structure preserving approximation of dissipative evolution problems}},
  volume={143},
  ISSN={0945-3245},
  DOI={10.1007/s00211-019-01050-w},
  number={1},
  journal={Numerische Mathematik},
  publisher={Springer Science and Business Media LLC},
  author={Egger, H.},
  year={2019},
  pages={85--106}
}

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