This paper contains the main ideas for an AMGe ( algebraic multigrid for fi
nite elements) method based on element agglomeration. In the method, coarse
grid elements are formed by agglomerating ne grid elements. Compatible int
erpolation operators are constructed which yield coarse grid basis function
s with a minimal energy property. Heuristics based on interpolation quality
measures are used to guide the agglomeration procedure. The performance of
the resulting method is demonstrated in two-level numerical experiments.