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Isogeometric analysis-based goal-oriented error estimation for free-boundary problems
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DOI：10.1016/j.finel.2010.12.013.png)
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Abstract
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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. (C) 2010 Elsevier B.V. All rights reserved.
Keywords:
Isogeometric analysis
Goal-oriented analysis
Bernoulli free boundary problem
B-splines
Non-uniform rational B-splines (NURBS)
T-splines
Bezier extraction
A posteriori error estimation
Shape-linearized adjoint
Duality
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