Abstract2018-05-24T12:52:58+00:00

eXtended Hybridizable Discontinuous Galerkin for incompressible flow problems with unfitted meshes and interfaces

Author (s): Gürkan, C; Kronbichler, M. and Fernández-Méndez, S.
Journal: International Journal for Numerical Methods in Engineering

Volume: 117
Pages: 756 – 777
Date: 2019

Abstract:
The eXtended Hybridizable Discontinuous Galerkin (X-HDG) method is developed for the solution of Stokes problems with void or material interfaces. X-HDG is a novel method that combines the Hybridizable Discontinuous Galerkin (HDG) method with an eXtended Finite Element (X-FEM) strategy, resulting in a high-order, unfitted, superconvergent method, with an explicit definition of the interface geometry by means of a level-set function.
For elements not cut by the interface, the standard HDG formulation is applied, whereas a modified weak form for the local problem is proposed for cut elements. Heaviside enrichment is considered on cut faces and in cut elements in the case of bimaterial problems.
Two-dimensional numerical examples demonstrate that the applicability, accuracy, and superconvergence properties of HDG are inherited in X-HDG, with the freedom of computational meshes that do not fit the interfaces.

  
  

Bibtex:

@article{doi:10.1002/nme.5975,
author = {Gürkan, Ceren and Kronbichler, Martin and Fernández-Méndez, Sonia},
title = {eXtended hybridizable discontinuous Galerkin for incompressible flow problems with unfitted meshes and interfaces},
journal = {International Journal for Numerical Methods in Engineering},
volume = {117},
number = {7},
pages = {756-777},
keywords = {bimaterial, high-order, hybridizable discontinuous Galerkin (HDG), interface, level-set, unfitted, void, X-FEM, X-HDG},
doi = {10.1002/nme.5975},
url = {https://onlinelibrary.wiley.com/doi/abs/10.1002/nme.5975},
eprint = {https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.5975},
abstract = {Summary The eXtended hybridizable discontinuous Galerkin (X-HDG) method is developed for the solution of Stokes problems with void or material interfaces. X-HDG is a novel method that combines the hybridizable discontinuous Galerkin (HDG) method with an eXtended finite element strategy, resulting in a high-order, unfitted, superconvergent method, with an explicit definition of the interface geometry by means of a level-set function. For elements not cut by the interface, the standard HDG formulation is applied, whereas a modified weak form for the local problem is proposed for cut elements. Heaviside enrichment is considered on cut faces and in cut elements in the case of bimaterial problems. Two-dimensional numerical examples demonstrate that the applicability, accuracy, and superconvergence properties of HDG are inherited in X-HDG, with the freedom of computational meshes that do not fit the interfaces},,
year = {2019}
}