SFB 1313 Publication "Consistent and Asymptotic-Preserving Finite-Volume Robin Transmission Conditions for Singularly Perturbed Elliptic Equations"

New SFB 1313 publication, published in the book Domain Decomposition Methods in Science and Engineering XXVI. The work has been developed within the SFB 1313 research project B03.

"Consistent and Asymptotic-Preserving Finite-Volume Robin Transmission Conditions for Singularly Perturbed Elliptic Equations" pp 443–450

Authors

• Martin J. Gander (Université de Genève)
• Stephan B. Lunowa (Technical University of Munich, former SFB 1313 partner member)
• Christian Rohde (University of Stuttgart, SFB 1313 research projects B03 and C02)

Abstract

Adaptive Dirichlet–Neumann and Robin–Neumann algorithms for singularlyperturbed advection-diffusion equations were introduced in [2], accounting for transport along characteristics, see also [6] for the discrete setting and damped versions using a modified quadrature rule to recover the hyperbolic limit. Non-overlapping Schwarz DDMs with Robin transmission conditions (TCs) applied to advectiondiffusion equations were analyzed in [1, 10] and a stabilized finite-element method for singularly perturbed problems was discussed in [9], see also [3, 4] and references therein for heterogeneous couplings. However, the behavior of these DDMs in the limit of vanishing diffusion has not been addressed.