Adaptive isogeometric analysis based on locally refined Tchebycheffian B-splines

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 on the particularly interesting class of Tchebycheffian splines whose pieces belong to null-spaces of constant-coefficient linear differential operators. They offer the freedom of combining algebraic polynomials with exponential and trigonometric functions, with any number of individual shape parameters, and have been recently equipped with efficient evaluation and manipulation procedures. We consider their application in the context of isogeometric analysis and discuss related adaptive refinement, adopting the so-called structured mesh refinement strategy, widely used and analyzed in the classical polynomial case.