Trigonometric b-spline quasi-interpolants and their applications to numerical integration and elliptic PDEs

Abstract

This work presents the construction and analysis of trigonometric B-splines of orders 2, 3, and 4 for numerical approximation. We develop associated quasi-interpolants and weighted Gaussian quadrature rules, and demonstrate their effectiveness in computing the L2-energy of functions. Additionally, these tools are applied to solve a second-order elliptic differential equation with homogeneous boundary conditions using a classical variational formulation. Numerical experiments confirm the accuracy, stability, and efficiency of the proposed methods.