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Licensed Unlicensed Requires Authentication Published by De Gruyter October 11, 2023

A Conforming Virtual Element Method for Parabolic Integro-Differential Equations

  • Sangita Yadav ORCID logo EMAIL logo , Meghana Suthar and Sarvesh Kumar

Abstract

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 L 2 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.

MSC 2010: 65M15; 65N12; 65N15

Award Identifier / Grant number: CRG/2020/001599

Award Identifier / Grant number: 1044/(CSIR-UGC NET DEC.2018)

Funding statement: The first author would like to thank the Department of Science and Technology (DST-SERB) India (grant number CRG/2020/001599) for supporting the work. The second author would like to thank to CSIR for financial support with 1044/(CSIR-UGC NET DEC.2018).

Acknowledgements

We would like to thank Prof. Amiya K. Pani for his valuable suggestions and comments in the preparation of this manuscript.

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Received: 2022-10-21
Revised: 2023-06-21
Accepted: 2023-09-01
Published Online: 2023-10-11
Published in Print: 2024-10-01

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