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A discontinuous‐Galerkin‐based immersed boundary method
Author(s) -
Lew Adrián J.,
Buscaglia Gustavo C.
Publication year - 2008
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.2312
Subject(s) - discontinuous galerkin method , mathematics , boundary (topology) , dirichlet boundary condition , polygon mesh , finite element method , boundary value problem , galerkin method , partial differential equation , robin boundary condition , mathematical analysis , domain (mathematical analysis) , free boundary problem , mixed boundary condition , geometry , physics , thermodynamics
A numerical method to approximate partial differential equations on meshes that do not conform to the domain boundaries is introduced. The proposed method is conceptually simple and free of user‐defined parameters. Starting with a conforming finite element mesh, the key ingredient is to switch those elements intersected by the Dirichlet boundary to a discontinuous‐Galerkin approximation and impose the Dirichlet boundary conditions strongly. By virtue of relaxing the continuity constraint at those elements, boundary locking is avoided and optimal‐order convergence is achieved. This is shown through numerical experiments in reaction–diffusion problems. Copyright © 2008 John Wiley & Sons, Ltd.