Imposing dirichlet boundary conditions with Nitsche's method and spline-based finite elements

TitleImposing dirichlet boundary conditions with Nitsche's method and spline-based finite elements
Publication TypeJournal Article
Year of Publication2010
AuthorsA Embar, J Dolbow, and I Harari
JournalInternational Journal for Numerical Methods in Engineering
Volume83
Issue7
Start Page877
Pagination877 - 898
Date Published08/2010
Abstract

A key challenge while employing non-interpolatory basis functions in finite-element methods is the robust imposition of Dirichlet boundary conditions. The current work studies the weak enforcement of such conditions for B-spline basis functions, with application to both second-and fourth-order problems. This is achieved using concepts borrowed from Nitsche's method, which is a stabilized method for imposing constraints on surfaces. Conditions for the stability of the system of equations are derived for each class of problem. Stability parameters in the Nitsche weak form are then evaluated by solving a local generalized eigenvalue problem at the Dirichlet boundary. The approach is designed to work equally well when the grid used to build the splines conforms to the physical boundary of interest as well as to the more general case when it does not. Through several numerical examples, the approach is shown to yield optimal rates of convergence. © 2010 John Wiley & Sons, Ltd.

DOI10.1002/nme.2863
Short TitleInternational Journal for Numerical Methods in Engineering