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Calcolo
Published in: Calcolo 4/2023

01-11-2023

A numerical method for analysis and simulation of diffusive viscous wave equations with variable coefficients on polygonal meshes

Authors: Naresh Kumar, Bhupen Deka

Published in: Calcolo | Issue 4/2023

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Abstract

In this study, we design and analyze weak Galerkin finite element methods to approximate diffusive viscus wave equations with variable coefficients on polygonal meshes. The proposed method has numerous assets, including supporting a higher order of convergence and general polygonal meshes. We investigated the convergence analysis using a two-step technique that discretizes first in space and then in time. A second-order Newmark scheme is employed to develop the temporal discretization and obtain the optimal order of convergence rate in \(L^{\infty }(L^2)\) and \(L^{\infty }(H^1)\) norms. In other words, we attain \({{\mathcal {O}}}(h^{k+1}+\tau ^2)\) in \(L^{\infty }(L^2)\) norm and \({{\mathcal {O}}}(h^{k}+\tau ^2)\) in \(L^{\infty }(H^1)\) norm. We performed several numerical experiments in a two-dimensional setting, illustrating our theoretical convergence findings.
previous article A streamline-derivative-based local projection stabilization virtual element method for nonlinear convection–diffusion–reaction equation
next article Preconditioning of discrete state- and control-constrained optimal control convection-diffusion problems
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Metadata
Title
A numerical method for analysis and simulation of diffusive viscous wave equations with variable coefficients on polygonal meshes
Authors
Naresh Kumar
Bhupen Deka
Publication date
01-11-2023
Publisher
Springer International Publishing
Published in
Calcolo / Issue 4/2023
Print ISSN: 0008-0624
Electronic ISSN: 1126-5434
DOI
https://doi.org/10.1007/s10092-023-00541-5

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