A Conforming Virtual Element Method for Parabolic Integro-Differential Equations-Reference-Cited by-同舟云学术

A Conforming Virtual Element Method for Parabolic Integro-Differential Equations

Published:2023-10-11 Issue:0 Volume:0 Page:
ISSN:1609-4840
Container-title:Computational Methods in Applied Mathematics
language:en
Short-container-title:

Author:

Yadav Sangita¹^ORCID,Suthar Meghana¹,Kumar Sarvesh²

Affiliation:

1. Department of Mathematics , Birla Institute of Technology and Science , Pilani , Pilani Campus , India

2. Department of Mathematics , Indian Institute of Space Science and Technology , Thiruvananthapuram , India

Abstract

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

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.

Funder

Department of Science and Technology, Ministry of Science and Technology, India

Council of Scientific and Industrial Research, India

Publisher

Walter de Gruyter GmbH

Subject

Applied Mathematics,Computational Mathematics,Numerical Analysis

Link

https://www.degruyter.com/document/doi/10.1515/cmam-2023-0061/pdf

Reference35 articles.

1. H. Aminikhah and J. Biazar, A new analytical method for solving systems of Volterra integral equations, Int. J. Comput. Math. 87 (2010), 1142–1157.

2. L. Beirão da Veiga, F. Brezzi, A. Cangiani, G. Manzini, L. D. Marini and A. Russo, Basic principles of virtual element methods, Math. Models Methods Appl. Sci. 23 (2013), no. 1, 199–214.

3. L. Beirão da Veiga, F. Brezzi, L. D. Marini and A. Russo, The hitchhiker’s guide to the virtual element method, Math. Models Methods Appl. Sci. 24 (2014), no. 8, 1541–1573.

4. L. Beirão da Veiga, F. Brezzi, L. D. Marini and A. Russo, Virtual element method for general second-order elliptic problems on polygonal meshes, Math. Models Methods Appl. Sci. 26 (2016), no. 4, 729–750.

5. J. R. Cannon and Y. P. Lin, A priori L 2 L^{2} error estimates for finite-element methods for nonlinear diffusion equations with memory, SIAM J. Numer. Anal. 27 (1990), no. 3, 595–607.

Cited by 1 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. Mixed virtual element method for integro-differential equations of parabolic type;Journal of Applied Mathematics and Computing;2024-04-16