A discontinuous-Galerkin-based immersed boundary method

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...

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Bibliographic Details
Published in:International journal for numerical methods in engineering 2008-10, Vol.76 (4), p.427-454
Main Authors: Lew, Adrián J., Buscaglia, Gustavo C.
Format: Article
Language:English
Subjects:
boundary locking
Cartesian grids
Computational techniques
Dirichlet conditions
discontinuous-Galerkin method
Exact sciences and technology
Fluid dynamics
Fundamental areas of phenomenology (including applications)
General theory
immersed boundary
immersed finite element method
interfaces
Mathematical methods in physics
Physics
Statistical physics, thermodynamics, and nonlinear dynamical systems
Transport processes
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Summary: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.
ISSN:0029-5981
1097-0207
DOI:10.1002/nme.2312