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Error profile for discontinuous Galerkin time stepping of parabolic PDEs

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Main Authors: William, McLean, Kassem, Mustapha
Format: Book
Language:English
Published: Springer 2023
Subjects:
discontinuous Galerkin
Online Access:https://link.springer.com/article/10.1007/s11075-022-01410-y
https://dlib.phenikaa-uni.edu.vn/handle/PNK/8300
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spelling oai:localhost:PNK-83002023-04-25T08:28:14Z Error profile for discontinuous Galerkin time stepping of parabolic PDEs William, McLean Kassem, Mustapha discontinuous Galerkin CC BY We consider the time discretization of a linear parabolic problem by the discontinuous Galerkin (DG) method using piecewise polynomials of degree at most r − 1 in t, for r ≥ 1 and with maximum step size k. It is well known that the spatial L2-norm of the DG error is of optimal order kr globally in time, and is, for r ≥ 2, superconvergent of order k2r− 1 at the nodes. We show that on the n th subinterval (tn− 1,tn), the dominant term in the DG error is proportional to the local right Radau polynomial of degree r. This error profile implies that the DG error is of order kr+ 1 at the right-hand Gauss–Radau quadrature points in each interval. We show that the norm of the jump in the DG solution at the left end point tn− 1 provides an accurate a posteriori estimate for the maximum error over the subinterval (tn− 1,tn). 2023-04-25T08:28:14Z 2023-04-25T08:28:14Z 2022 Book https://link.springer.com/article/10.1007/s11075-022-01410-y https://dlib.phenikaa-uni.edu.vn/handle/PNK/8300 en application/pdf Springer
institution Digital Phenikaa
collection Digital Phenikaa
language English
topic discontinuous Galerkin
spellingShingle discontinuous Galerkin
William, McLean
Kassem, Mustapha
Error profile for discontinuous Galerkin time stepping of parabolic PDEs
description CC BY
format Book
author William, McLean
Kassem, Mustapha
author_facet William, McLean
Kassem, Mustapha
author_sort William, McLean
title Error profile for discontinuous Galerkin time stepping of parabolic PDEs
title_short Error profile for discontinuous Galerkin time stepping of parabolic PDEs
title_full Error profile for discontinuous Galerkin time stepping of parabolic PDEs
title_fullStr Error profile for discontinuous Galerkin time stepping of parabolic PDEs
title_full_unstemmed Error profile for discontinuous Galerkin time stepping of parabolic PDEs
title_sort error profile for discontinuous galerkin time stepping of parabolic pdes
publisher Springer
publishDate 2023
url https://link.springer.com/article/10.1007/s11075-022-01410-y
https://dlib.phenikaa-uni.edu.vn/handle/PNK/8300
_version_ 1764177439413501952
score 8.887836

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