Isogeometric Analysis for singularly perturbed problems in 1-D: a numerical study
Numerical Analysis
2024-12-20 v1 Numerical Analysis
Abstract
We perform numerical experiments on one-dimensional singularly perturbed problems of reaction-convection-diffusion type, using isogeometric analysis. In particular, we use a Galerkin formulation with B-splines as basis functions. The question we address is: how should the knots be chosen in order to get uniform, exponential convergence in the maximum norm? We provide specific guidelines on how to achieve precisely this, for three different singularly perturbed problems.
Cite
@article{arxiv.1901.01949,
title = {Isogeometric Analysis for singularly perturbed problems in 1-D: a numerical study},
author = {Klio Liotati and Christos Xenophontos},
journal= {arXiv preprint arXiv:1901.01949},
year = {2024}
}