Minimal residual space-time discretizations of parabolic equations: Asymmetric spatial operators

We consider a minimal residual discretization of a simultaneous space-time variational formulation of parabolic evolution equations. Under the usual `LBB stability condition on pairs of trial- and test spaces we show quasi-optimality of the numerical approximations without assuming symmetry of the spatial part of the differential operator. Under a stronger LBB condition we show error estimates in an energy-norm which are independent of this spatial differential operator.