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Imposing Dirichlet boundary conditions in the extended finite element method
Author(s) -
Moës Nicolas,
Béchet Eric,
Tourbier Matthieu
Publication year - 2006
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.1675
Subject(s) - finite element method , dirichlet boundary condition , lagrange multiplier , boundary value problem , mathematics , boundary knot method , boundary (topology) , boundary conditions in cfd , discontinuity (linguistics) , mixed boundary condition , neumann boundary condition , rate of convergence , singular boundary method , mathematical analysis , robin boundary condition , computer science , boundary element method , mathematical optimization , structural engineering , engineering , key (lock) , computer security
This paper is devoted to the imposition of Dirichlet‐type conditions within the extended finite element method (X‐FEM). This method allows one to easily model surfaces of discontinuity or domain boundaries on a mesh not necessarily conforming to these surfaces. Imposing Neumann boundary conditions on boundaries running through the elements is straightforward and does preserve the optimal rate of convergence of the background mesh (observed numerically in earlier papers). On the contrary, much less work has been devoted to Dirichlet boundary conditions for the X‐FEM (or the limiting case of stiff boundary conditions). In this paper, we introduce a strategy to impose Dirichlet boundary conditions while preserving the optimal rate of convergence. The key aspect is the construction of the correct Lagrange multiplier space on the boundary. As an application, we suggest to use this new approach to impose precisely zero pressure on the moving resin front in resin transfer moulding (RTM) process while avoiding remeshing. The case of inner conditions is also discussed as well as two important practical cases: material interfaces and phase‐transformation front capturing. Copyright © 2006 John Wiley & Sons, Ltd.