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An ADI Finite Volume Element Method for a Viscous Wave Equation with Variable Coefficients
Mengya Su1, Zhihao Ren1, Zhiyue Zhang1, *
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 this 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.
Keywords
Cite This Article
Su, M., Ren, Z., Zhang, Z. (2020). An ADI Finite Volume Element Method for a Viscous Wave Equation with Variable Coefficients.
CMES-Computer Modeling in Engineering & Sciences, 123(2), 739–776. https://doi.org/10.32604/cmes.2020.08563
Citations