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Title: Overset meshing coupled with hybridizable discontinuous Galerkin finite elements

Abstract

We introduce the use of hybridizable discontinuous Galerkin (HDG) finite element methods on overlapping (overset) meshes. Overset mesh methods are advantageous for solving problems on complex geometrical domains. We also combine geometric flexibility of overset methods with the advantages of HDG methods: arbitrarily high-order accuracy, reduced size of the global discrete problem, and the ability to solve elliptic, parabolic, and/or hyperbolic problems with a unified form of discretization. This approach to developing the ‘overset HDG’ method is to couple the global solution from one mesh to the local solution on the overset mesh. We present numerical examples for steady convection–diffusion and static elasticity problems. The examples demonstrate optimal order convergence in all primal fields for an arbitrary amount of overlap of the underlying meshes.

Authors:
ORCiD logo [1];  [2];  [3]
  1. Pennsylvania State Univ., University Park, PA (United States). Applied Research Lab.; Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
  2. Pennsylvania State Univ., University Park, PA (United States). Applied Research Lab.
  3. Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
Publication Date:
Research Org.:
Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
Sponsoring Org.:
USDOE National Nuclear Security Administration (NNSA).
OSTI Identifier:
1399894
Report Number(s):
SAND2016-0713J
Journal ID: ISSN 0029-5981; 643547; TRN: US1702977
Grant/Contract Number:  
AC04-94AL85000
Resource Type:
Accepted Manuscript
Journal Name:
International Journal for Numerical Methods in Engineering
Additional Journal Information:
Journal Volume: 112; Journal Issue: 5; Journal ID: ISSN 0029-5981
Publisher:
Wiley
Country of Publication:
United States
Language:
English
Subject:
42 ENGINEERING; 97 MATHEMATICS AND COMPUTING; overset meshes; hybridizable discontinuous Galerkin; HDG; finite element; convection-diffusion; elasticity

Citation Formats

Kauffman, Justin A., Sheldon, Jason P., and Miller, Scott T.. Overset meshing coupled with hybridizable discontinuous Galerkin finite elements. United States: N. p., 2017. Web. https://doi.org/10.1002/nme.5512.
Kauffman, Justin A., Sheldon, Jason P., & Miller, Scott T.. Overset meshing coupled with hybridizable discontinuous Galerkin finite elements. United States. https://doi.org/10.1002/nme.5512
Kauffman, Justin A., Sheldon, Jason P., and Miller, Scott T.. Wed . "Overset meshing coupled with hybridizable discontinuous Galerkin finite elements". United States. https://doi.org/10.1002/nme.5512. https://www.osti.gov/servlets/purl/1399894.
@article{osti_1399894,
title = {Overset meshing coupled with hybridizable discontinuous Galerkin finite elements},
author = {Kauffman, Justin A. and Sheldon, Jason P. and Miller, Scott T.},
abstractNote = {We introduce the use of hybridizable discontinuous Galerkin (HDG) finite element methods on overlapping (overset) meshes. Overset mesh methods are advantageous for solving problems on complex geometrical domains. We also combine geometric flexibility of overset methods with the advantages of HDG methods: arbitrarily high-order accuracy, reduced size of the global discrete problem, and the ability to solve elliptic, parabolic, and/or hyperbolic problems with a unified form of discretization. This approach to developing the ‘overset HDG’ method is to couple the global solution from one mesh to the local solution on the overset mesh. We present numerical examples for steady convection–diffusion and static elasticity problems. The examples demonstrate optimal order convergence in all primal fields for an arbitrary amount of overlap of the underlying meshes.},
doi = {10.1002/nme.5512},
journal = {International Journal for Numerical Methods in Engineering},
number = 5,
volume = 112,
place = {United States},
year = {2017},
month = {3}
}

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