Higher order stable generalized isogeometric analysis for interface problems

Generalized isogeometric analysis (GIGA) enables accurate numerical solutions for interface problem with optimal convergence rates. However, the approach is not stable in terms of the spline functions’ degree and is not robust with the position of the interface. In this paper, we introduce a stable GIGA (SGIGA) through a specific modification of the enrichment space. We prove that SGIGA can retain optimal convergence rates, and provide necessary well-conditioning for arbitrary degree and arbitrary location of the interface. We validate the theoretical results in various illustrations and compare the method with the stable generalized finite element method and GIGA.