Error profile for discontinuous Galerkin time stepping of parabolic PDEs
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Springer
2023
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| Truy cập trực tuyến: | https://link.springer.com/article/10.1007/s11075-022-01410-y https://dlib.phenikaa-uni.edu.vn/handle/PNK/8300 |
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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 |
8.891145 |