We begin the mathematical study of Isogeometric Analysis based on NURBS (non-uniform rational B-splines.) Isogeometric Analysis is a generalization of classical Finite Element Analysis (FEA) which… (More)

Based on the local refinement algorithm addressed in [18], we analyze the linear independence of the bi-cubic T-spline blending functions corresponding to particular T-meshes.

We initiate the study of efficient quadrature rules for NURBS -based isogeometric analysis. A rule of thumb emerges, the “half-point rule”, indicat ng that optimal rules involve a number of points… (More)

We develop new quadrature rules for Isogeometric Analysis based on the solution of a local nonlinear problem. A simple and robust algorithm is developed to determine the rules which are exact for… (More)

We introduce a new discretization scheme for Maxwell equations in two space dimension. Inspired by the new paradigm of Isogeometric analysis introduced in [16], we propose an algorithm based on the… (More)

We study the discretization behavior of classical finite ele ment and NURBS approximations on problems of structural vibrations and wave propaga tion. We find that, on the basis of equal numbers of… (More)

We prove the stability and a priori global and local error analysis for the residual-free bubbles finite element method applied to advection dominated advection-diffusion problems.

We derive an explicit formula for the fine-scale Green’s function arising in variational multiscale analysis. The formula is expressed in terms of the classical Green’s function and a projector which… (More)