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

Anand Embar, John Dolbow*, Isaac Harari

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

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.

Original languageEnglish
Pages (from-to)877-898
Number of pages22
JournalInternational Journal for Numerical Methods in Engineering
Volume83
Issue number7
DOIs
StatePublished - 13 Aug 2010

Funding

FundersFunder number
National Science Foundation0825839

    Keywords

    • B-splines
    • Dirichlet BCs
    • Fourth-order problems
    • Nitsche's method

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