A Conforming Virtual Element Method for Parabolic Integro-Differential Equations

This article develops and analyses a conforming virtual element scheme for the spatial discretization of parabolic integro-differential equations combined with backward Euler’s scheme for temporal discretization. With the help of Ritz–Voltera and projection operators, optimal a priori error estimate...

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Bibliographic Details
Published inJournal of computational methods in applied mathematics Vol. 24; no. 4; pp. 1001 - 1019
Main Authors Yadav, Sangita, Suthar, Meghana, Kumar, Sarvesh
Format Journal Article
LanguageEnglish
Published Minsk De Gruyter 01.10.2024
Walter de Gruyter GmbH
Subjects
65M15
65N12
65N15
Differential equations
Discretization
Error Estimates
Mathematics
Parabolic Integro-Differential Equation
Variational Formulation
Virtual Element Method
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Summary:This article develops and analyses a conforming virtual element scheme for the spatial discretization of parabolic integro-differential equations combined with backward Euler’s scheme for temporal discretization. With the help of Ritz–Voltera and projection operators, optimal a priori error estimates are established. Moreover, several numerical experiments are presented to confirm the computational efficiency of the proposed scheme and validate the theoretical findings.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
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ISSN:1609-4840
1609-9389
DOI:10.1515/cmam-2023-0061