The Influence of Quadrature Errors on Isogeometric Mortar Methods

TL;DR

This paper examines how quadrature errors affect the accuracy of isogeometric mortar methods, analyzing different quadrature schemes and their impact on convergence and stability.

Contribution

It provides a mathematical analysis of quadrature-induced variational crimes in isogeometric mortar methods and compares the effects of different quadrature rules.

Findings

Quadrature errors can reduce convergence rates.

Using combined quadrature rules mitigates the impact of variational crimes.

Non-symmetric saddle point problems are introduced by certain quadrature choices.

Abstract

Mortar methods have recently been shown to be well suited for isogeometric analysis. We review the recent mathematical analysis and then investigate the variational crime introduced by quadrature formulas for the coupling integrals. Motivated by finite element observations, we consider a quadrature rule purely based on the slave mesh as well as a method using quadrature rules based on the slave mesh and on the master mesh, resulting in a non-symmetric saddle point problem. While in the first case reduced convergence rates can be observed, in the second case the influence of the variational crime is less significant.