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Galerkin approximations of an abstract parabolic boundary value problem with "rough" boundary data are considered. The optimal rates of convergence in      L p [ 0 T ; L 2 ( Ω  ) ] {L_p}[0T;{L_2}(\Omega )]       norms for      L p [ 0 T ; L 2 ( Γ  ) ] {L_p}[0T;{L_2}(\Gamma )]       boundary terms are derived.

Galerkin approximations of abstract parabolic boundary value problems with rough boundary data—𝐿_{𝑝} theory