An enriched discontinuous Galerkin formulation for the coupling of non-conforming meshes

G. Haikal, Keith Hjelmstad

Research output: Contribution to journalArticle

8 Citations (Scopus)

Abstract

Finite element modeling using non-conforming meshes requires an interface model that ensures geometric compatibility and a complete transfer of surface tractions between the connecting elements at the non-conforming interfaces. Most currently available coupling methods are dual approaches that employ a field of Lagrange multipliers to enforce geometric compatibility at the interface. The choice of the Lagrange multiplier field is not trivial since not all possible interpolations satisfy the inf-sup or Ladyzhenskaya-Babuška-Brezzi (LBB) condition. The primal discontinuous Galerkin (DG) and Nitsche methods are not subject to the LBB restrictions, however, in both these methods a mesh-dependent penalty parameter is required to ensure stability [24,2]. We propose a primal interface formulation that makes use of a local enrichment of the interface elements to enable an unbiased enforcement of geometric compatibility at all interface nodes without inducing over-constraint and without introducing additional variables. We show that a local DG-based interface stabilization procedure guarantees a consistent transfer of the traction field across the non-conforming interface.

Original languageEnglish (US)
Pages (from-to)496-503
Number of pages8
JournalFinite Elements in Analysis and Design
Volume46
Issue number6
DOIs
StatePublished - Jun 2010

Fingerprint

Discontinuous Galerkin
Lagrange multipliers
Mesh
Formulation
Interpolation
Compatibility
Stabilization
Nitsche's Method
Interface Element
Coupling Method
Finite Element Modeling
Discontinuous Galerkin Method
Penalty
Trivial
Interpolate
Restriction
Dependent
Vertex of a graph

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics
  • Engineering(all)
  • Computer Graphics and Computer-Aided Design

Cite this

An enriched discontinuous Galerkin formulation for the coupling of non-conforming meshes. / Haikal, G.; Hjelmstad, Keith.

In: Finite Elements in Analysis and Design, Vol. 46, No. 6, 06.2010, p. 496-503.

Research output: Contribution to journalArticle

@article{9841a367ff874c53b49a5a43e6e43b11,
title = "An enriched discontinuous Galerkin formulation for the coupling of non-conforming meshes",
abstract = "Finite element modeling using non-conforming meshes requires an interface model that ensures geometric compatibility and a complete transfer of surface tractions between the connecting elements at the non-conforming interfaces. Most currently available coupling methods are dual approaches that employ a field of Lagrange multipliers to enforce geometric compatibility at the interface. The choice of the Lagrange multiplier field is not trivial since not all possible interpolations satisfy the inf-sup or Ladyzhenskaya-Babuška-Brezzi (LBB) condition. The primal discontinuous Galerkin (DG) and Nitsche methods are not subject to the LBB restrictions, however, in both these methods a mesh-dependent penalty parameter is required to ensure stability [24,2]. We propose a primal interface formulation that makes use of a local enrichment of the interface elements to enable an unbiased enforcement of geometric compatibility at all interface nodes without inducing over-constraint and without introducing additional variables. We show that a local DG-based interface stabilization procedure guarantees a consistent transfer of the traction field across the non-conforming interface.",
author = "G. Haikal and Keith Hjelmstad",
year = "2010",
month = "6",
doi = "10.1016/j.finel.2009.12.008",
language = "English (US)",
volume = "46",
pages = "496--503",
journal = "Finite Elements in Analysis and Design",
issn = "0168-874X",
publisher = "Elsevier",
number = "6",

}

TY - JOUR

T1 - An enriched discontinuous Galerkin formulation for the coupling of non-conforming meshes

AU - Haikal, G.

AU - Hjelmstad, Keith

PY - 2010/6

Y1 - 2010/6

N2 - Finite element modeling using non-conforming meshes requires an interface model that ensures geometric compatibility and a complete transfer of surface tractions between the connecting elements at the non-conforming interfaces. Most currently available coupling methods are dual approaches that employ a field of Lagrange multipliers to enforce geometric compatibility at the interface. The choice of the Lagrange multiplier field is not trivial since not all possible interpolations satisfy the inf-sup or Ladyzhenskaya-Babuška-Brezzi (LBB) condition. The primal discontinuous Galerkin (DG) and Nitsche methods are not subject to the LBB restrictions, however, in both these methods a mesh-dependent penalty parameter is required to ensure stability [24,2]. We propose a primal interface formulation that makes use of a local enrichment of the interface elements to enable an unbiased enforcement of geometric compatibility at all interface nodes without inducing over-constraint and without introducing additional variables. We show that a local DG-based interface stabilization procedure guarantees a consistent transfer of the traction field across the non-conforming interface.

AB - Finite element modeling using non-conforming meshes requires an interface model that ensures geometric compatibility and a complete transfer of surface tractions between the connecting elements at the non-conforming interfaces. Most currently available coupling methods are dual approaches that employ a field of Lagrange multipliers to enforce geometric compatibility at the interface. The choice of the Lagrange multiplier field is not trivial since not all possible interpolations satisfy the inf-sup or Ladyzhenskaya-Babuška-Brezzi (LBB) condition. The primal discontinuous Galerkin (DG) and Nitsche methods are not subject to the LBB restrictions, however, in both these methods a mesh-dependent penalty parameter is required to ensure stability [24,2]. We propose a primal interface formulation that makes use of a local enrichment of the interface elements to enable an unbiased enforcement of geometric compatibility at all interface nodes without inducing over-constraint and without introducing additional variables. We show that a local DG-based interface stabilization procedure guarantees a consistent transfer of the traction field across the non-conforming interface.

UR - http://www.scopus.com/inward/record.url?scp=77949918326&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=77949918326&partnerID=8YFLogxK

U2 - 10.1016/j.finel.2009.12.008

DO - 10.1016/j.finel.2009.12.008

M3 - Article

VL - 46

SP - 496

EP - 503

JO - Finite Elements in Analysis and Design

JF - Finite Elements in Analysis and Design

SN - 0168-874X

IS - 6

ER -