Equivalence between the DPG method and the exponential integrators for linear parabolic problems

Tipo de publicación
Artículo en revista
Autores

Judit Muñoz-Matute, David Pardo, Leszek Demkowicz

Abstract

The Discontinuous Petrov-Galerkin (DPG) method and the exponential integrators are two well established numerical methods for solving Partial Differential Equations (PDEs) and stiff systems of Ordinary Differential Equations (ODEs), respectively. In this work, we apply the DPG method in the time variable for linear parabolic problems and we calculate the optimal test functions analytically. We show that the DPG method in time is equivalent to exponential integrators for the trace variables, which are decoupled from the interior variables. In addition, the DPG optimal test functions allow us to compute the approximated solutions in the time element interiors. This DPG method in time allows to construct a posteriori error estimations in order to perform adaptivity. We generalize this novel DPG-based time-marching scheme to general first order linear systems of ODEs. We show the performance of the proposed method for 1D and 2D + time linear parabolic PDEs after discretizing in space by the finite element method.

Conferencia / Revista
Journal of Computational Physics
Editor
Elsevier
Año de publicación
2021
Cita bibliográfica

Judit Muñoz-Matute, David Pardo, Leszek Demkowicz,
Equivalence between the DPG method and the exponential integrators for linear parabolic problems,
Journal of Computational Physics,
Volume 429,
2021,
110016,
ISSN 0021-9991,
https://doi.org/10.1016/j.jcp.2020.110016

DOI
https://doi.org/10.1016/j.jcp.2020.110016