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ARTICLE

An ADI Finite Volume Element Method for a Viscous Wave Equation with Variable Coefficients

Mengya Su¹, Zhihao Ren¹, Zhiyue Zhang^{1, *}

1 School of Mathematical Sciences, Jiangsu Provincial Key Laboratory for Numerical Simulation of Large Scale Complex Systems, Nanjing Normal University, Nanjing, 210023, China.

* Corresponding Author: Zhiyue Zhang. Email: .

(This article belongs to the Special Issue: Numerical Methods for Differential and Integral Equations)

Computer Modeling in Engineering & Sciences 2020, 123(2), 739-776. https://doi.org/10.32604/cmes.2020.08563

Received 08 September 2019; Accepted 29 November 2019; Issue published 01 May 2020

Abstract

Based on rectangular partition and bilinear interpolation, we construct an alternating-direction implicit (ADI) finite volume element method, which combined the merits of finite volume element method and alternating direction implicit method to solve a viscous wave equation with variable coefficients. This paper presents a general procedure to construct the alternating-direction implicit finite volume element method and gives computational schemes. Optimal error estimate in L² norm is obtained for the schemes. Compared with the finite volume element method of the same convergence order, our method is more effective in terms of running time with the increasing of the computing scale. Numerical experiments are presented to show the efficiency of our method and numerical results are provided to support our theoretical analysis.

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