CVEM-BEM Coupling with Decoupled Orders for 2D Exterior Poisson Problems
Luca Desiderio, Silvia Falletta, Matteo Ferrari, L. Scuderi
Abstract
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 $$\textit{L}^\text {2}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mi>L</mml:mi> <mml:mtext>2</mml:mtext> </mml:msup> </mml:math> -norm, in which the CVEM and BEM contributions to the error are separated. This allows for 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.