Combining DPG in space with DPG time-marching scheme for the transient advection–reaction equation

Munoz-Matute, Judit; Demkowicz, Leszek; Roberts, Nathan V.

doi:10.1016/j.cma.2022.115471

Title: Combining DPG in space with DPG time-marching scheme for the transient advection–reaction equation

Journal Article · Mon Aug 22 00:00:00 EDT 2022 · Computer Methods in Applied Mechanics and Engineering

DOI:https://doi.org/10.1016/j.cma.2022.115471· OSTI ID:1888552

^[1]; Demkowicz, Leszek ^[2]; Roberts, Nathan V. ^[3]

Basque Center for Applied Mathematics (BCAM), Bilbao (Spain); Univ. of Texas, Austin, TX (United States)
Univ. of Texas, Austin, TX (United States)
Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)

In this article, we present a general methodology to combine the Discontinuous Petrov–Galerkin (DPG) method in space and time in the context of methods of lines for transient advection–reaction problems. We first introduce a semidiscretization in space with a DPG method redefining the ideas of optimal testing and practicality of the method in this context. Then, we apply the recently developed DPG-based time-marching scheme, which is of exponential-type, to the resulting system of Ordinary Differential Equations (ODEs). Further, we also discuss how to efficiently compute the action of the exponential of the matrix coming from the space semidiscretization without assembling the full matrix. Finally, we verify the proposed method for 1D+time advection–reaction problems showing optimal convergence rates for smooth solutions and more stable results for linear conservation laws comparing to the classical exponential integrators.

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Research Organization:: Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)

Sponsoring Organization:: USDOE National Nuclear Security Administration (NNSA); European Union (EU); National Science Foundation (NSF); USDOE Laboratory Directed Research and Development (LDRD) Program

Grant/Contract Number:: NA0003525; 777778 (MATHROCKS); 1819101

OSTI ID:: 1888552

Report Number(s):: SAND2022-10828J; 708980

Journal Information:: Computer Methods in Applied Mechanics and Engineering, Vol. 402; ISSN 0045-7825

Publisher:: ElsevierCopyright Statement

Country of Publication:: United States

Language:: English

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