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Mixed Virtual Element Method for Linear Parabolic Integro-Differential Equations

Mixed Virtual Element Method for Linear Parabolic Integro-Differential Equations

Year:    2024

Author:    Meghana Suthar, Sangita Yadav

International Journal of Numerical Analysis and Modeling, Vol. 21 (2024), Iss. 4 : pp. 504–527

Abstract

This article develops and analyses a mixed virtual element scheme for the spatial discretization of linear parabolic integro-differential equations (PIDEs) combined with backward Euler’s temporal discretization approach. The introduction of mixed Ritz-Volterra projection significantly helps in managing the integral terms, yielding optimal convergence of order O(hk+1) for the two unknowns p(x,t) and σ(x,t). In addition, a step-by-step analysis is proposed for the super convergence of the discrete solution of order O(hk+2). The fully discrete case has also been analyzed and discussed to achieve O(τ) in time. Several computational experiments are discussed to validate the proposed schemes computational efficiency and support the theoretical conclusions.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/ijnam2024-1020

International Journal of Numerical Analysis and Modeling, Vol. 21 (2024), Iss. 4 : pp. 504–527

Published online:    2024-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    24

Keywords:    Mixed virtual element method parabolic integro-differential equation error estimates super-convergence.

Author Details

Meghana Suthar Email

Sangita Yadav Email