Adaptive refinement with locally linearly independent LR B-splines: Theory and applications
Francesco Patrizi, Carla Manni, Francesca Pelosi, Hendrik Speleers
Abstract
In this paper, we describe an adaptive refinement strategy for LR B-splines. The presented strategy ensures, at each iteration, local linear independence of the obtained set of LR B-splines. This property is then exploited in two applications: the construction of efficient quasi-interpolation schemes and the numerical solution of elliptic problems using the isogeometric Galerkin method.
Topics & Concepts
MathematicsInterpolation (computer graphics)Isogeometric analysisApplied mathematicsGalerkin methodIndependence (probability theory)Linear interpolationMathematical optimizationAdaptive mesh refinementFinite element methodMathematical analysisComputer scienceComputational scienceStatisticsPhysicsAnimationPolynomialComputer graphics (images)ThermodynamicsAdvanced Numerical Analysis TechniquesPolynomial and algebraic computation