@article{68bf8c9a5f5149b9b29f27f09d5fc807, title = "An analysis of the practical DPG method", abstract = "Abstract. We give a complete error analysis of the Discontinuous Petrov Galerkin (DPG) method, accounting for all the approximations made in its practical implementation. Specifically, we consider the DPG method that uses a trial space consisting of polynomials of degree p on each mesh element. Earlier works showed that there is a {"}trial-to-test{"} operator T, which when applied to the trial space, defines a test space that guarantees stability. In DPG formulations, this operator T is local: it can be applied element-by-element. However, an infinite dimensional problem on each mesh element needed to be solved to apply T. In practical computations, T is approximated using polynomials of some degree r ≥ p on each mesh element. We show that this approximation maintains optimal convergence rates, provided that r > p+N, where N is the space dimension (two or more), for the Laplace equation. We also prove a similar result for the DPG method for linear elasticity. Remarks on the conditioning of the stiffness matrix in DPG methods are also included. {\textcopyright} 2013 American Mathematical Society.", keywords = "Discontinuous galerkin, DPG method, Petrov-Galerkin, Ultraweak formulation", author = "J. Gopalakrishnan and W. Qiu", year = "2014", month = mar, doi = "10.1090/S0025-5718-2013-02721-4", language = "English", volume = "83", pages = "537--552", journal = "Mathematics of Computation", issn = "0025-5718", publisher = "American Mathematical Society", number = "286", }