Discontinuous Galerkin Isogeometric Analysis for The Biharmonic Equation

TL;DR

This paper introduces a discontinuous Galerkin isogeometric analysis method for solving the biharmonic equation on multi-patch domains, providing theoretical error estimates and numerical validation.

Contribution

The paper develops a novel dG-IgA method for biharmonic problems on complex domains with multiple patches, including error analysis and numerical experiments.

Findings

Error estimates in a discrete norm are established.

Numerical experiments confirm the theoretical convergence rates.

The method effectively handles multi-patch geometries.

Abstract

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.

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See pages 1-last of dGBiharmonic_Moore_CMWA_Review