This paper reviews the state of the art and discusses recent developments in the field of
adaptive isogeometric analysis, with special focus on the mathematical theory. This includes …

Background: Curved modeling technology originated from the geometric lofting and design
of aircrafts, automobiles and ships. The control points of the traditional B-spline mesh should …

We introduce locally refined (LR) Tchebycheffian B-splines as a generalization of LR B-
splines from the algebraic polynomial setting to the broad Tchebycheffian setting. We focus …

Univariate generalized splines are smooth piecewise functions with sections in certain
extended Tchebycheff spaces. They are a natural extension of univariate (algebraic) …

In this paper, we survey the use of generalized B-splines in isogeometric Galerkin and
collocation methods. Generalized B-splines are a special class of Tchebycheffian B-splines …

In this paper we define Tchebycheffian spline spaces over planar T-meshes and we address
the problem of determining their dimension. We extend to the Tchebycheffian spline context …

Highlights are the following: For any integer, we construct‐continuous partition of unity (PU)
functions with flat‐top from B‐spline functions to have numerical solutions of fourth‐order …

Univariate generalized splines are smooth piecewise functions with sections in certain
extended Tchebycheff spaces. They are a natural extension of univariate (algebraic) …

This paper reviews the state of the art and discusses recent developments in the field of
adaptive isogeometric analysis, with special focus on the mathematical theory. This includes …

Generalized splines are smooth functions belonging piecewisely to spaces which are a
natural generalization of algebraic polynomials. GB-splines are a B-spline-like basis for …