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.
SOLUTIONS AND STABILITY ANALYSIS OF BACKWARD-EULER METHOD FOR SIMPLIFIED MAGNETOHYDRODYNAMICS WITH NONLINEAR TIME RELAXATION
