About: A Posteriori Error Estimates for Fully Discrete Finite Element Method for Generalized Diffusion Equation with Delay

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An Entity of Type : schema:ScholarlyArticle, within Data Space : wasabi.inria.fr associated with source document(s)

Attributes	Values
type	Academic Article research paper schema:ScholarlyArticle
isDefinedBy	Covid-on-the-Web dataset
has title	A Posteriori Error Estimates for Fully Discrete Finite Element Method for Generalized Diffusion Equation with Delay
Creator	Wang, Wansheng Xiao, Aiguo Yi, Lijun
Source	Medline; PMC
abstract	In this paper, we derive several a posteriori error estimators for generalized diffusion equation with delay in a convex polygonal domain. The Crank–Nicolson method for time discretization is used and a continuous, piecewise linear finite element space is employed for the space discretization. The a posteriori error estimators corresponding to space discretization are derived by using the interpolation estimates. Two different continuous, piecewise quadratic reconstructions are used to obtain the error due to the time discretization. To estimate the error in the approximation of the delay term, linear approximations of the delay term are used in a crucial way. As a consequence, a posteriori upper and lower error bounds for fully discrete approximation are derived for the first time. In particular, long-time a posteriori error estimates are obtained for stable systems. Numerical experiments are presented which confirm our theoretical results.
has issue date	2020-07-01(xsd:dateTime)
bibo:doi	10.1007/s10915-020-01262-5
bibo:pmid	32834471
has license	no-cc
sha1sum (hex)	52ba4a6657074605f67e64a394f45c739c5e0ca8
schema:url	https://doi.org/10.1007/s10915-020-01262-5
resource representing a document's title	A Posteriori Error Estimates for Fully Discrete Finite Element Method for Generalized Diffusion Equation with Delay
has PubMed Central identifier	PMC7327226
has PubMed identifier	32834471
schema:publication	J Sci Comput
resource representing a document's body	covid:52ba4a6657074605f67e64a394f45c739c5e0ca8#body_text
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