Simultaneous quasi‐optimal convergence rates in FEM‐BEM coupling. (25th March 2015)

• Record Type: Journal Article
• Authors: Melenk, J. M.; Praetorius, D.; Wohlmuth, B.
• Other Names: Dauge Monique guestEditor.; Nicaise Serge guestEditor.
• Is Part Of: Mathematical methods in the applied sciences. Volume 40:Number 2(2017)
• Page Start: 463
• Page End: 485
• Publication Date: 2015-03-25
• Subjects: FEM‐BEM coupling -- a priori convergence analysis -- transmission problem; Mathematics -- Periodicals; Technology -- Mathematics -- Periodicals; 519
• DOI: 10.1002/mma.3374
• Languages: English
• ISSNs: 0170-4214

Abstract

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.