We revisit the finite element analysis of convection dominated flow problems within the
recently developed Discontinuous Petrov-Galerkin (DPG) variational framework. We
demonstrate how test function spaces that guarantee numerical stability can be computed
automatically with respect to the so called optimal test space norm by using an element
subgrid discretization. This should make the DPG method not only stable but also robust,
that is, uniformly stable with respect to the Ṕeclet number in the current application. The …

We revisit the finite element analysis of convection-dominated flow problems within the
recently developed Discontinuous Petrov–Galerkin (DPG) variational framework. We
demonstrate how test function spaces that guarantee numerical stability can be computed
automatically with respect to the optimal test space norm. This makes the DPG method not
only stable but also robust, that is, uniformly stable with respect to the Péclet number in the
current application. We employ discontinuous piecewise Bernstein polynomials as trial …