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Error representation of the time-marching DPG scheme
Muñoz-Matute, J.
; Demkowicz, Leszek; Pardo, D. (2022-03-01)
; Demkowicz, Leszek; Pardo, D. (2022-03-01)
In this article, we introduce an error representation function to perform adaptivity in time of the recently developed time-marching Discontinuous Petrov–Galerkin (DPG) scheme. We first provide an analytical expression for ...
A DPG-based time-marching scheme for linear hyperbolic problems
Muñoz-Matute, J.; Pardo, D.; Demkowicz, L. (2020-11)
; Pardo, D.; Demkowicz, L. (2020-11)
The Discontinuous Petrov-Galerkin (DPG) method is a widely employed discretization method for Partial Di fferential Equations (PDEs). In a recent work, we applied the DPG method with optimal test functions for the time ...
Equivalence between the DPG method and the Exponential Integrators for linear parabolic problems
Muñoz-Matute, J.; Pardo, D.; Demkowicz, L. (2020-11)
; Pardo, D.; Demkowicz, L. (2020-11)
The Discontinuous Petrov-Galerkin (DPG) method and the exponential integrators are two well established numerical methods for solving Partial Di fferential Equations (PDEs) and sti ff systems of Ordinary Di fferential ...