Analysis of Backward Euler Primal DPG Methods

Abstract We analyze backward Euler time stepping schemes for a primal DPG formulation of class parabolic problems. Optimal error estimates are shown in natural norm and the L 2 {L^{2}} field variable. For heat equation solution our equals standard Galerkin scheme and, thus, optimal bounds found literature. In presence advection reaction terms, however, latter identity is not valid anymore analysis requires to resort elliptic projection operators. It essential that these operators be projections with respect spatial part PDE, as schemes, full PDE at step, done previously.