Abstract
Isogeometric analysis (IGA), introduced in 2005 by T.J. R Hughes, replaces traditional Finite Elements with element descriptions using tensor product 3-varaite NonUniform Rational B-splines (NURBS), thus combining the exact topology description in Finite Element Analysis with the accurate shape representation in Computer Aided Design. NURBS based IGA shows great promise; however, NURBS lack the necessary local refinement needed. Locally Refined splines (LR B-splines), such as T-splines and the novel Locally Refined B-splines (LR B-splines) show great promise with respect to the needed local refinement. The talk will address IGA, and LR B-splines, and report on the work on the theoretical basis of LR B-splines.