Residual-free bubbles for embedded Dirichlet problems

TitleResidual-free bubbles for embedded Dirichlet problems
Publication TypeJournal Article
Year of Publication2008
AuthorsJE Dolbow, and LP Franca
JournalComputer Methods in Applied Mechanics and Engineering
Volume197
Issue45-48
Start Page3751
Pagination3751 - 3759
Date Published08/2008
Abstract

We examine a stabilized method employing residual-free bubbles for enforcing Dirichlet constraints on embedded finite element interfaces. In particular, we focus attention on problems where the underlying mesh is not explicitly "fitted" to the geometry of the interface. The residual-free bubble problem is derived for a simple case and extensions are discussed. We show that under certain conditions, stabilization only requires knowledge of the residual-free bubble on the interface. We then examine methods to approximate the residual-free bubble. A series of benchmark tests are used to demonstrate the accuracy and robustness of the method. Comparisons are made to Nitsche's method employing an eigenvalue estimate for the global stability parameter. Particular emphasis is placed on the accuracy of flux evaluations on the interface. Finally, we employ the method to simulate an evolving interface problem motivated by resin transfer molding. © 2008 Elsevier B.V. All rights reserved.

DOI10.1016/j.cma.2008.02.033
Short TitleComputer Methods in Applied Mechanics and Engineering