Discontinuous Galerkin Isogeometric Analysis for The Biharmonic Equation
It extends isogeometric analysis to handle C^1-continuous problems on non-conforming multi-patch geometries for computational mechanics.
The paper develops and analyzes a discontinuous Galerkin isogeometric analysis method for solving the biharmonic equation on multi-patch domains, providing a priori error estimates and numerical validation.
We present and analyze an interior penalty discontinuous Galerkin Isogeometric Analysis (dG-IgA) method for the biharmonic equation in computational domain in $\mathbb{R}^d$ with $d =2,3.$ The computational domain consist of several non-overlapping sub-domains or patches. We construct B-Spline approximation spaces which are discontinuous across patch interfaces. We present a priori error estimate in a discrete norm and numerical experiments to confirm the theory.