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lkogler wrote: "degree, nDoF, L2 err (l2 proj), l2 err - lDirect solve, l2 err-GMRES with multigrid prec, GMRES iter"
It looks like you are using the multigrid preconditioner.
That means "real" geometric multigrid for the lowest order space only, plus a block-smoother to take care of the high order space. The low order system on the coarsest mesh is solved exactly.
So, with order=1 and without mesh refinement, the multigrid preconditioner is just the direct inverse and GMRes converges in one iteration.