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An unfitted discontinuous Galerkin scheme for conservation laws on evolving surfaces

Proceedings of ALGORITMY 2016, 20th Conference on Scientific Computing, Vysoke Tatry, Podbanske, Slovakia, March 13-18, 2016, page 44--54 - 2016
Télécharger la publication : 1602.01080v1.pdf [1Mo]  
Motivated by considering partial differential equations arising from conservation laws posed on evolving surfaces, a new numerical method for an advection problem is developed and simple numerical tests are performed. The method is based on an unfitted discontinuous Galerkin approach where the surface is not explicitly tracked by the mesh which means the method is extremely flexible with respect to geometry. Furthermore, the discontinuous Galerkin approach is well-suited to capture the advection driven by the evolution of the surface without the need for a space-time formulation, back-tracking trajectories or streamline diffusion. The method is illustrated by a one-dimensional example and numerical results are presented that show good convergence properties for a simple test problem.

Références BibTex

@InProceedings{ERW16,
  author       = {Engwer, C. and Ranner, T. and Westerheide, S.},
  title        = {An unfitted discontinuous Galerkin scheme for conservation laws on evolving surfaces},
  booktitle    = {Proceedings of ALGORITMY 2016, 20th Conference on Scientific Computing, Vysoke Tatry, Podbanske, Slovakia, March 13-18, 2016},
  pages        = {44--54},
  year         = {2016},
  editor       = {Handlovi\čova, A. and Sev\čovi\č, D.},
  publisher    = {Publishing House of Slovak University of Technology in Bratislava},
  note         = {http://www.iam.fmph.uniba.sk/amuc/ojs/index.php/algoritmy/article/view/393 and arXiv e-print (arXiv:1602.01080) (02/2016)},
  keywords     = {discontinuous Garlerkin, unfitted finite elements, surface partial differential equations, conservation laws},
  issn         = {978-80-227-4454-4},
  url          = \{/2016/ERW16},
}

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