Simultaneous quasi-optimal convergence in FEM-BEM coupling

On linear ODEs with a time singularity of the rst kind and unsmooth inhomo-geneity 6/2014 A degenerate fourth-order parabolic equation modeling Bose-Einstein condensation. We consider the symmetric FEM-BEM 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 by an integral equation on the coupling boundary Γ = ∂Ω. We assume that the corresponding transmission problem admits a shift theorem by more than 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, while 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).