CVEM-BEM Coupling with Decoupled Orders for 2D Exterior Poisson Problems

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 $$\textit{L}^\text {2}$$ L 2 -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.

A virtual element method for the solution of 2D time-harmonic elastic wave equations via scalar potentials

“…Proof. The proof is similar to those of [26,Lemma 4.6] and [32,Theorem 4.1]. In particular, existence and uniqueness of q h ∈ V k h , solution of (34), follow from ( 23) and (25), which entail the ellipticity and continuity of Āh in V(Ω) and in V k h .…”