Discontinuous Petrov‐Galerkin Methods for the 1D Babuška‐Ihlenburg Problem

In this paper we consider two least‐squares methods: the discontinuous Petrov‐Galerkin method and a new version of the hybridized discontinuous Petrov‐Galerkin method. The aim of this paper is to compute the optimal test functions for these methods in the Babuška‐Ihlenburg problem in 1D. The optimal test functions will be computed with respect to the chosen inner product spaces and bilinear forms. We shall show numerical results of h‐convergence of the methods.