CVEM-BEM coupling with decoupled orders for 2D exterior Poisson problems

TL;DR

This paper introduces a novel coupling of the Curved Virtual Element Method with Boundary Element Method for 2D exterior Poisson problems, enabling high accuracy with decoupled approximation orders.

Contribution

It presents a new CVEM-BEM coupling approach with decoupled orders, providing optimal error estimates and improved computational flexibility.

Findings

Numerical results confirm the theoretical error estimates.

The approach achieves high accuracy with low order BEM.

Decoupled orders enhance computational efficiency.

Abstract

For the solution of 2D exterior Dirichlet Poisson problems we propose the coupling of a Curved Virtual Element Method (CVEM) with a Boundary Element Method (BEM), by using decoupled approximation orders. We provide optimal convergence error estimates, in the energy and in the weaker $\textit{L}^\text{2}$-norm, in which the CVEM and BEM contributions to the error are separated. This allows taking advantage of the high order flexibility of the CVEM to retrieve an accurate discrete solution by using a low order BEM. The numerical results confirm the a priori estimates and show the effectiveness of the proposed approach.