| Title:
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Unified error analysis of discontinuous Galerkin methods for parabolic obstacle problem (English) |
| Author:
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Majumder, Papri |
| Language:
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English |
| Journal:
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Applications of Mathematics |
| ISSN:
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0862-7940 (print) |
| ISSN:
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1572-9109 (online) |
| Volume:
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66 |
| Issue:
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5 |
| Year:
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2021 |
| Pages:
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673-699 |
| Summary lang:
|
English |
| . |
| Category:
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math |
| . |
| Summary:
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We introduce and study various discontinuous Galerkin (DG) finite element approximations for a parabolic variational inequality associated with a general obstacle problem in $\mathbb {R}^d$ $(d=2,3)$. For the fully-discrete DG scheme, we employ a piecewise linear finite element space for spatial discretization, whereas the time discretization is carried out with the implicit backward Euler method. We present a unified error analysis for all well known symmetric and non-symmetric DG fully discrete schemes, and derive error estimate of optimal order $\mathcal {O}(h+\Delta t)$ in an energy norm. Moreover, the analysis is performed without any assumptions on the speed of propagation of the free boundary and only the realistic regularity $u_t\in \mathcal {L}^2(0,T; \mathcal {L}^2(\Omega ))$ is assumed. Further, we present some numerical experiments to illustrate the performance of the proposed methods. (English) |
| Keyword:
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finite element |
| Keyword:
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discontinuous Galerkin method |
| Keyword:
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parabolic obstacle problem |
| MSC:
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65N15 |
| MSC:
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65N30 |
| idZBL:
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07396173 |
| idMR:
|
MR4299880 |
| DOI:
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10.21136/AM.2021.0030-20 |
| . |
| Date available:
|
2021-08-18T08:29:14Z |
| Last updated:
|
2023-11-06 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/149078 |
| . |
| Reference:
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