B-spline goal-oriented error estimators for geometrically nonlinear rods
TEXAS UNIV AT AUSTIN INST FOR COMPUTATIONAL ENGINEERING AND SCIENCES
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We consider goal-oriented a posteriori error estimators for the evaluation of the errors on quantities of interest associated with the solution of geometrically nonlinear curved elastic rods. For the numerical solution of these nonlinear one-dimensional problems, we adopt a B-spline based Galerkin method, a particular case of the more general Isogeometric Analysis. We propose error estimators using higher order enhanced solutions, which are based on the concept of enrichment of the original B-spline basis by means of the pure kappa-refinement procedure typical of Isogeometric Analysis. We provide several numerical examples for linear and nonlinear output functionals, corresponding to the rotation, displacements and strain energy of the rod, and we compare the effectiveness of the proposed error estimators.
- Numerical Mathematics