Abstract:
We analyze multigrid convergence when 2D-elliptic boundary value problems with interfaces are discretized
using finite element methods where coarse meshes do not approximate the interface geometry. Starting with
the initial mesh, the used interface adapted mesh generator constructs a finite element mesh up to a certain
refinement level where the interface lines are approximated with a sufficient precision. It is shown that multigrid
cycles based on SOR-smoothing and specific interpolation and restriction operators converge independently of
the meshsize parameter. Moreover, in practice the convergence is also independent of the ratio of the jumping
coefficients. We demonstrate the efficiency of our method by means of numerical examples.
Fulltext:
PDF file (1270 kB)