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Overset meshing coupled with hybridizable discontinuous Galerkin finite elements
Author(s) -
Kauffman Justin A.,
Sheldon Jason P.,
Miller Scott T.
Publication year - 2017
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.5512
Subject(s) - discontinuous galerkin method , polygon mesh , discretization , finite element method , mathematics , parameterized complexity , convergence (economics) , mathematical optimization , computer science , mathematical analysis , algorithm , geometry , physics , economics , thermodynamics , economic growth
Summary 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 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. Our 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. Copyright © 2017 John Wiley & Sons, Ltd.