Bild

Isogeometric analysis for singularly perturbed problems in 1-D: error estimates

    Christos Xenophontos, Irene Sykopetritou

ETNA - Electronic Transactions on Numerical Analysis, pp. 1-25, 2020/01/16

doi: 10.1553/etna_vol52s1

doi: 10.1553/etna_vol52s1


PDF
X
BibTEX-Export:

X
EndNote/Zotero-Export:

X
RIS-Export:

X 
Researchgate-Export (COinS)

Permanent QR-Code

doi:10.1553/etna_vol52s1



doi:10.1553/etna_vol52s1

Abstract

We consider one-dimensional singularly perturbed boundary value problems of reaction-convection-diffusion type, and the approximation of their solution using isogeometric analysis. In particular, we use a Galerkin formulation with B-splines as basis functions, defined on appropriately chosen knot vectors. We prove robust exponential convergence in the energy norm, independently of the singular perturbation parameters, and illustrate our findings through a numerical example.

Keywords: singularly perturbed problem, reaction-convection-diffusion, boundary layers, isogeometric analysis, robust exponential convergence