Simultaneous quasi‐optimal convergence rates in FEM‐BEM coupling. (25th March 2015) - Melenk, J. M.; Praetorius, D.; Wohlmuth, B.
Abstract : S. Nicaise We consider the symmetric finite element–boundary element coupling that connects two linear elliptic second‐order partial differential equations posed in a bounded domain Ω and its complement, where the exterior problem is restated as an integral equation on the coupling boundary Γ = ∂ Ω. Under the assumption that the corresponding transmission problem admits a shift theorem for data in H −1 + s, s ∈[0, s 0 ], s 0 >1/2, we analyze the discretization by piecewise polynomials of degree k for the domain variable and piecewise polynomials of degree k − 1 for the flux variable on the coupling boundary. Given sufficient regularity, we show that (up to logarithmic factors) the optimal convergence O ( h k + 1/2 ) in the H −1/2 ( Γ )‐norm is obtained for the flux variable, whereas classical arguments by Céa‐type quasi‐optimality and standard approximation results provide only O ( h k ) for the overall error in the natural product norm on H 1 (Ω) × H −1/2 ( Γ ). Copyright © 2015 John Wiley & Sons, Ltd.