Christoph Erath, Günther Of, Francisco-Javier Sayas
Published 2015-09-01Version 1
As model problem we consider the prototype for flow and transport of a concentration in porous media in an interior domain and couple it with a diffusion process in the corresponding unbounded exterior domain. To solve the problem we develop a new non-symmetric coupling between the vertex-centered finite volume and boundary element method. This discretization provides naturally conservation of local fluxes and with an upwind option also stability in the convection dominated case. We aim to provide a first rigorous analysis of the system for different model parameters; stability, convergence, and a~priori estimates. This includes the use of an implicit stabilization, known from the finite element and boundary element method coupling. Some numerical experiments conclude the work and confirm the theoretical results.
Comments: finite volume method, boundary element method, non-symmetric coupling, convection dominated, existence and uniqueness, convergence, a priori estimate
Mortar coupling of $hp$-discontinuous Galerkin and boundary element methods for the Helmholtz equation
Functional a posteriori error estimates for boundary element methods
Stable non-symmetric coupling of the finite volume and the boundary element method for convection-dominated parabolic-elliptic interface problems
![QR code for arXiv:1509.00440 [math.NA]](http://oss.arxitics.com/images/favicon.svg)