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We analyse backward Euler time stepping schemes for the primal DPGformulation of a class of parabolic problems. Optimal error estimates are shownin the natural norm and in the $L^2$ norm of the field variable. For the heatequation the solution of our primal DPG formulation equals the solution of astandard Galerkin scheme and, thus, optimal error bounds are found in theliterature. In the presence of advection and reaction terms, however, thelatter identity is not valid anymore and the analysis of optimal error boundsrequires to resort to elliptic projection operators. It is essential that theseoperators be projections with respect to the spatial part of the PDE, as instandard Galerkin schemes, and not with respect to the full PDE at a time step,as done previously.

Analysis of backward Euler primal DPG methods