Isogeometric analysis-based goal-oriented error estimation for free-boundary problems

Authors:
K. G. van der Zee;C. V. Verhoosel
Affiliations:
Institute for Computational Engineering and Sciences (ICES), The University of Texas at Austin, 201 East 24th Street, 1 University Station C0200, Austin, TX 78712, USA;Department of Mechanical Engineering, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlands
Venue:
Finite Elements in Analysis and Design
Year:
2011

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Abstract

We consider goal-oriented error estimation for free-boundary problems using isogeometric analysis. Goal-oriented methods require the solution of the dual problem, which is a problem for the adjoint of the linearized free-boundary problem. Owing to linearization, this dual problem includes a curvature-dependent boundary condition, which leads to cumbersome implementations if the discrete free boundary is only continuous, as in a piecewise-linear representation. Isogeometric finite elements straightforwardly provide continuously differentiable free boundaries for which the corresponding dual problem can be easily implemented. We illustrate the computation of the linearized-adjoint problems with two test cases and estimate the error in corresponding quantities of interest. In the first problem, a single B-spline patch can be employed. In the second problem, we employ T-splines. Bezier extraction is used to provide a finite element interface to these two distinct spline technologies.