Abstract
In this paper, we establish a rigorous a priori error analysis for Isogeometric Analysis (IGA) applied to second-order elliptic interface problems discretized with non-matching B-spline patches. Interface problems with discontinuous diffusion coefficients and complex geometric boundaries are ubiquitous in multi-material modeling and composite structures. By leveraging B-spline and Non-Uniform Rational B-Spline (NURBS) basis functions, the proposed framework represents the exact interface geometry while permitting independent mesh refinement and polynomial degrees across patch boundaries. Coupling across non-conforming interface subdomains is enforced weakly through a weighted Nitsche-type formulation incorporating flux averages and penalty terms adapted to local inverse inequalities and coefficient contrasts. We prove that the method is coercive and stable under standard mesh assumptions, and we derive optimal a priori error estimates in both the energy norm and the $L^2$-norm, achieving convergence orders of $\mathcal{O}(h^p)$ and $\mathcal{O}(h^{p+1})$ for B-spline discretizations of degree $p$. Numerical benchmark problems featuring curved interfaces, non-matching knot vectors, and steep conductivity jumps are presented to validate the theoretical error bounds and demonstrate the efficiency and robustness of the computational scheme.
