Discontinuous Petrov-Galerkin method based on the optimal test space norm for one-dimensional transport problems

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 Peclet number in the current application. The effectiveness of the algorithm is demonstrated on two problems for the linear advection-diffusion equation.