Boundary elements for clamped Kirchhoff--Love plates

TL;DR

This paper introduces a Galerkin boundary element method for clamped Kirchhoff--Love plates, achieving optimal convergence and handling piecewise smooth boundaries with explicit operator representations and numerical validation.

Contribution

It develops a direct boundary element method based on the representation formula, with trace approximation spaces of arbitrary order and explicit boundary integral operators.

Findings

Method is quasi-optimal in the trace norm.

Achieves optimal convergence order under minimal regularity.

Numerical experiments confirm theoretical convergence rates.

Abstract

We present a Galerkin boundary element method for clamped Kirchhoff--Love plates with piecewise smooth boundary. It is a direct method based on the representation formula and requires the inversion of the single-layer operator and an application of the double-layer operator to the Dirichlet data. We present trace approximation spaces of arbitrary order, required for both the Dirichlet data and the unknown Neumann trace. Our boundary element method is quasi-optimal with respect to the natural trace norm and achieves optimal convergence order under minimal regularity assumptions. We provide explicit representations of both boundary integral operators and discuss the implementation of the appearing integrals. Numerical experiments for smooth and non-smooth domains confirm predicted convergence rates.