Veröffentlichungen und Präsentationen

It is well known that the convergence rate of a numerical model is significantly reduced, when the genuine character of the setting with differential equation and boundary condition is not given anymore. Here we examine the decrease of convergence order for models using COMSOL in which the problem set-up includes a coupling between a 1D and a 2D subdomain. In terms of physics we are dealing with flow in the vicinity of a fracture in a porous medium. We study two different set-ups, one within a (potentially) unbounded domain, and one in a bounded domain between two impermeable strata. We examine the convergence rates for different physical parameter sets, for different finite elements, and different error norms. It turns out that the convergence rate is significantly reduced. Moreover it turns out to be independent of element order – an indication that the combined geometry and not the finite element discretisation is the bottleneck in this type of model.