AbstractMany problems in electrical engineering or fluid mechanics can be
modeled by parabolic-elliptic interface problems,
where the domain for the exterior elliptic problem might be unbounded.
A possibility to solve this class of problems numerically is
the non-symmetric coupling of finite elements (FEM) and boundary elements (BEM)
analyzed in [H. Egger, C. Erath and R. Schorr,
On the nonsymmetric coupling method for parabolic-elliptic interface problems,
SIAM J. Numer. Anal. 56 2018, 6, 3510–3533].
If, for example, the interior problem represents a fluid,
this method is not appropriate
since FEM in general lacks conservation of numerical fluxes and in case of
convection dominance also stability.
A possible remedy to guarantee both is the use
of the vertex-centered finite volume method (FVM) with an
upwind stabilization option.
Thus, we propose a (non-symmetric) coupling of FVM and BEM for a semi-discretization of the
underlying problem. For the subsequent time discretization we introduce two
options: a variant
of the backward Euler method which allows us to develop an analysis under minimal regularity assumptions
and the classical backward Euler method.
We analyze both, the semi-discrete and the fully-discrete system, in terms of convergence
and error estimates. Some numerical examples illustrate the theoretical findings and
give some ideas for practical applications.
Stochastic Galerkin methods for elliptic interface problems with random input
