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Original Articles

A combined finite element method for parabolic equations posted in domains with rough boundaries

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Pages 1908-1927 | Received 17 Aug 2018, Accepted 19 Aug 2019, Published online: 02 Oct 2019
 

Abstract

In this paper, we consider the solution of parabolic equations posted in domains with rough boundaries using the combined finite element procedure proposed in Xu et al. [A combined finite element method for elliptic problems posted in domains with rough boundaries, J. Comput. Appl. Math. 336 (2018), pp. 235–248] in space and backward-Euler scheme in time. We first prove L2 error estimates for elliptic projection operator Rh,H for both β=1 and β=1 by the dual argument which depend on the elliptic auxiliary problem, and then energy error estimates of semi-discrete and fully discrete schemes which have convergence rates about O(H)+O(hs) and O(H)+O(hs)+O(Δt), where s>0, respectively. Numerical results are provided for parabolic equations in domains with non-oscillating or oscillating boundaries to verify the theoretical findings.

2010 Mathematics Subject Classifications:

Acknowledgements

The authors would like to thank the referees for their careful reading and constructive comments that improved the paper.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

The work of the authors was partially supported by the PhD Scientific Research Foundation of Jiangxi Science and Technology Normal University [grant number 2018BSQD009], the National Natural Science Foundation of China [grant number 61802157], and the Scientific Research Fund of Jiangxi Provincial Education Department [grant number GJJ180626].

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