A DPG-based time-marching scheme for linear hyperbolic problems

Type of publication
Article de presse
Auteurs

Judit Muñoz-Matute, David Pardo, Leszek Demkowicz

Abstract

The Discontinuous Petrov–Galerkin (DPG) method is a widely employed discretization method for Partial Differential Equations (PDEs). In a recent work, we applied the DPG method with optimal test functions for the time integration of transient parabolic PDEs. We showed that the resulting DPG-based time-marching scheme is equivalent to exponential integrators for the trace variables. In this work, we extend the aforementioned method to time-dependent hyperbolic PDEs. For that, we reduce the second order system in time to first order and we calculate the optimal testing analytically. We also relate our method with exponential integrators of Gautschi-type. Finally, we validate our method for 1D/2D + time linear wave equation after semidiscretization in space with a standard Bubnov–Galerkin method. The presented DPG-based time integrator provides expressions for the solution in the element interiors in addition to those on the traces. This allows to design different error estimators to perform adaptivity.

Conférence / Magazine
Computer Methods in Applied Mechanics and Engineering
Éditeur
Springer
Année de publication
2021
Citation bibliographique

Judit Muñoz-Matute, David Pardo, Leszek Demkowicz,
A DPG-based time-marching scheme for linear hyperbolic problems,
Computer Methods in Applied Mechanics and Engineering,
Volume 373,
2021,
113539,
ISSN 0045-7825,
https://doi.org/10.1016/j.cma.2020.113539

DOI
https://doi.org/10.1016/j.cma.2020.113539