Isogeometric analysis for singularly perturbed high-order, two-point boundary value problems of reaction–diffusion type

Abstract

We consider two-point, reaction–diffusion type, singularly perturbed boundary value problems of order 2ν∈Z+, and the approximation of their solution using isogeometric analysis. In particular, we use a Galerkin formulation with B-splines as basis functions, defined using appropriately chosen knot vectors. We prove robust exponential convergence in the energy norm, independently of the singular perturbation parameter. Numerical examples are also presented, which illustrate (and extend) the theory.