A Nitsche-based domain decomposition method for hypersingular integral equations

TL;DR

This paper presents a Nitsche-based domain decomposition method for hypersingular integral equations that enables non-matching grid discretizations without Lagrangian multipliers, demonstrating near-optimal convergence through theoretical analysis and numerical experiments.

Contribution

The paper introduces a novel Nitsche-based approach for hypersingular integral equations that avoids Lagrangian multipliers and handles non-matching grids, with proven convergence.

Findings

Achieves almost quasi-optimal convergence

Enables discretizations with non-matching grids

Validated by numerical experiments

Abstract

We introduce and analyze a Nitsche-based domain decomposition method for the solution of hypersingular integral equations. This method allows for discretizations with non-matching grids without the necessity of a Lagrangian multiplier, as opposed to the traditional mortar method. We prove its almost quasi-optimal convergence and underline the theory by a numerical experiment.