Isogeometric mortar methods

TL;DR

This paper investigates isogeometric mortar methods, presenting stable spline space pairings for Lagrange multipliers, with theoretical proofs and numerical validation of their stability and performance.

Contribution

It introduces two stable spline space pairings for isogeometric mortar methods, including one that avoids cross point modifications, supported by theoretical analysis and numerical experiments.

Findings

Both spline space pairings are inf-sup stable.

The pairing without cross point modification is proven stable.

Numerical examples confirm theoretical stability and effectiveness.

Abstract

The application of mortar methods in the framework of isogeometric analysis is investigated theoretically as well as numerically. For the Lagrange multiplier two choices of uniformly stable spaces are presented, both of them are spline spaces but of a different degree. In one case, we consider an equal order pairing for which a cross point modification based on a local degree reduction is required. In the other case, the degree of the dual space is reduced by two compared to the primal. This pairing is proven to be inf-sup stable without any necessary cross point modification. Several numerical examples confirm the theoretical results and illustrate additional aspects. Keywords: isogeometric analysis, mortar methods, inf-sup stability, cross point modification.