Interior Estimates of Semidiscrete Finite Element Methods for Parabolic Problems with Distributional Data
Year: 2019
Author: Li Guo, Hengguang Li, Yang Yang
Journal of Computational Mathematics, Vol. 37 (2019), Iss. 4 : pp. 458–474
Abstract
Let $Ω ⊂ \mathbb{R}^d$, $1 ≤ d ≤ 3$, be a bounded $d$-polytope. Consider the parabolic equation on $Ω$ with the Dirac delta function on the right hand side. We study the well-posedness, regularity, and the interior error estimate of semidiscrete finite element approximations of the equation. In particular, we derive that the interior error is bounded by the best local approximation error, the negative norms of the error, and the negative norms of the time derivative of the error. This result implies different convergence rates for the numerical solution in different interior regions, especially when the region is close to the singular point. Numerical test results are reported to support the theoretical prediction.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jcm.1804-m2017-0240
Journal of Computational Mathematics, Vol. 37 (2019), Iss. 4 : pp. 458–474
Published online: 2019-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 17
Keywords: Parabolic problems Distributional data Finite element methods Interior estimates Well-posedness Singularity.
Author Details
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Guo, Li
Li, Hengguang
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SIAM Journal on Numerical Analysis, Vol. 57 (2019), Iss. 5 P.2246
https://doi.org/10.1137/18M1197746 [Citations: 2]