Matched $G^k$-constructions yield $C^k$-continuous iso-geometric elements

TL;DR

This paper demonstrates how geometrically continuous surface constructions can produce $C^k$ iso-geometric elements even at irregular mesh points with complex element junctions.

Contribution

It introduces a method to achieve $C^k$ continuity in iso-geometric elements at irregular quad mesh points using $G^k$ constructions.

Findings

$C^k$ iso-geometric elements are achievable at irregular mesh points.

The method extends iso-geometric analysis to complex mesh topologies.

Enhanced continuity improves geometric and analysis accuracy.

Abstract

The note shows how $G^k$ (geometrically continuous surface) constructions yield $C^k$ iso-geometric elements also at irregular quad mesh points where three or more than four elements come together.