# Discontinuous Galerkin Isogeometric Analysis for Elliptic Problems with Discontinuous Coefficients on Surfaces

## TL;DR

This paper extends discontinuous Galerkin isogeometric analysis to handle elliptic surface problems with discontinuous coefficients and non-matching meshes, providing theoretical error estimates and numerical validation.

## Contribution

It generalizes a priori error estimates to non-matching meshes and discontinuous coefficients on surfaces, advancing the applicability of dGIGA in practical scenarios.

## Key findings

- Error estimates are validated through numerical experiments.
- The method effectively handles discontinuities across patch interfaces.
- The approach accommodates non-matching meshes in surface problems.

## Abstract

This paper is concerned with using discontinuous Galerkin isogeometric analysis (dGIGA) as a numerical treatment of Diffusion problems on orientable surfaces $\Omega \subset \mathbb{R}^3$. The computational domain or surface considered consist of several non-overlapping sub-domains or patches which are coupled via an interior penalty scheme. In Langer and Moore U. Langer and S. E. Moore,2014, we presented a priori error estimate for conforming computational domains with matching meshes across patch interface and a constant diffusion coefficient. However, in this article, we generalize the \textit{a priori} error estimate to non-matching meshes and discontinuous diffusion coefficients across patch interfaces commonly occurring in industry. We construct B-Spline or NURBS approximation spaces which are discontinuous across patch interfaces. We present \textit{a priori} error estimate for the symmetric discontinuous Galerkin scheme and numerical experiments to confirm the theory.