TY - JOUR

T1 - Isogeometric analysis-based goal-oriented error estimation for free-boundary problems

AU - Zee, van der, K.G.

AU - Verhoosel, C.V.

PY - 2011

Y1 - 2011

N2 - 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. Bézier extraction is used to provide a finite element interface to these two distinct spline technologies.

AB - 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. Bézier extraction is used to provide a finite element interface to these two distinct spline technologies.

U2 - 10.1016/j.finel.2010.12.013

DO - 10.1016/j.finel.2010.12.013

M3 - Article

VL - 47

SP - 600

EP - 609

JO - Finite Elements in Analysis and Design

JF - Finite Elements in Analysis and Design

SN - 0168-874X

IS - 6

ER -