Judit Muñoz-Matute

The University of Texas at Austin, USA.

We present a time-marching scheme based on the Discontinuous Petrov-Galerkin method with optimal test functions for linear transient problems. For that, we employ an ultraweak variational formulation and we show that the scheme is equivalent to exponential integrators for the trace variables. Additionally, our method delivers the L^2 projection of the solution in the element interiors and an error representation function for adaptivity in time. We combine our method in time with Bubnov-Galerkin discretization in space. We show the performance of the method and adaptive strategy for 1D and 2D + time linear Partial Differential Equations. We show the performance of our method for 1D and 2D + time linear hyperbolic problems together with an algorithm to speed up the computation of exponential-related functions.