ILYA LASHUK
COARSE DE RHAM COMPLEXES WITH IMPROVED APPROXIMATION PROPERTIES

7000 East Ave
L-560
LIVERMORE
CA
94550
LASHUK2@LLNL.GOV
PANAYOT VASSILEVSKI

We present a technique based on element agglomeration for constructing coarse subspaces of: (a) the lowest order tetrahedral Nédélec  space, and (b) the scalar piecewise-linear finite element space, in both cases assuming general unstructured mesh. The constructed coarse spaces, together with coarse $H(\mathbf{div})$ and $L_2$ spaces described in our previous work, form an exact sequence with respect to the exterior derivative operators (for domains homeomorphic to a ball). The constructed coarse counterparts of the Nédélec  and Raviart-Thomas spaces locally contain the vector constant functions, whereas the respective coarse version of the scalar piecewise-linear space locally contains all linear functions. These properties hold regardless of the shape of the agglomerates, as long as each agglomerate stays homeomorphic to a ball (which is easily ensured in practice). We illustrate the approximation properties of the constructed coarse spaces as well as the convergence of respective two-level AMGe methods associated with them.