A robust DPG method for large domains

Robust DPG Method for Convection-Dominated Diffusion Problems

A Spacetime Dpg Method for Acoustic Waves

A spacetime discontinuous Petrov-Galerkin (DPG) method for the linear wave equation is presented. This method is based on a weak formulation that uses a broken graph space. The wellposedness of this formulation is established using a previously presented abstract framework. One of the main tasks in the verification of the conditions of this framework is proving a density result. This is done in...

The DPG method for the Stokes problem

We discuss well-posedness and convergence theory for the DPG method applied to a general system of linear Partial Differential Equations (PDEs) and specialize the results to the classical Stokes problem. The Stokes problem is an iconic troublemaker for standard Bubnov Galerkin methods; if discretizations are not carefully designed, they may exhibit non-convergence or locking. By contrast, DPG d...

A Spacetime DPG Method for the Schrödinger Equation

A spacetime Discontinuous Petrov Galerkin (DPG) method for the linear timedependent Schrödinger equation is proposed. The spacetime approach is particularly attractive for capturing irregular solutions. Motivated by the fact that some irregular Schrödinger solutions cannot be solutions of certain first order reformulations, the proposed spacetime method uses the second order Schrödinger operato...

A primal DPG method without a first-order reformulation

We show that it is possible to apply the DPG methodology without reformulating a second order boundary value problem into a first order system, by considering the simple example of the Poisson equation. The result is a new weak formulation and a new DPG method for the Poisson equation, which has no numerical trace variable, but has a numerical flux approximation on the element interfaces, in ad...