A discontinuous-Galerkin-based immersed boundary method

• Published in: International journal for numerical methods in engineering Vol. 76; no. 4; pp. 427 - 454
• Main Authors: Lew, Adrián J., Buscaglia, Gustavo C.
• Format: Journal Article
• Language: English
• Published: Chichester, UK John Wiley & Sons, Ltd 22-10-2008; Wiley
• 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; Discontinuity; interfaces; Computational fluid dynamics; Cartesian grids; Fluid-structure interactions; Immersed boundary method; Reaction diffusion equation; Experimental study; Galerkin-Petrov method; Finite element method; discontinuous-Galerkin method; boundary locking; immersed boundary; immersed finite element method; Dirichlet conditions; Dirichlet problem; Boundary-value problems; Diffusion equation; Modelling; Boundary element method; Cartesian coordinates
• ISSN: 0029-5981; 1097-0207
• DOI: 10.1002/nme.2312

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.