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Volume 5, Issue 1
Finite Volume Element Method for Second Order Hyperbolic Equations

S. Kumar, N. Nataraj & A. K. Pani

Int. J. Numer. Anal. Mod., 5 (2008), pp. 132-151.

Published online: 2008-05

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  • Abstract

We discuss a priori error estimates for a semidiscrete piecewise linear finite volume element (FVE) approximation to a second order wave equation in a two-dimensional convex polygonal domain. Since the domain is convex polygonal, a special attention has been paid to the limited regularity of the exact solution. Optimal error estimates in $L^2$, $H^1$ norms and quasi-optimal estimates in $L^∞$ norm are discussed without quadrature and also with numerical quadrature. Numerical results confirm the theoretical order of convergence.

  • AMS Subject Headings

65N30, 65N15

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COPYRIGHT: © Global Science Press

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@Article{IJNAM-5-132, author = {}, title = {Finite Volume Element Method for Second Order Hyperbolic Equations}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2008}, volume = {5}, number = {1}, pages = {132--151}, abstract = {

We discuss a priori error estimates for a semidiscrete piecewise linear finite volume element (FVE) approximation to a second order wave equation in a two-dimensional convex polygonal domain. Since the domain is convex polygonal, a special attention has been paid to the limited regularity of the exact solution. Optimal error estimates in $L^2$, $H^1$ norms and quasi-optimal estimates in $L^∞$ norm are discussed without quadrature and also with numerical quadrature. Numerical results confirm the theoretical order of convergence.

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/803.html} }
TY - JOUR T1 - Finite Volume Element Method for Second Order Hyperbolic Equations JO - International Journal of Numerical Analysis and Modeling VL - 1 SP - 132 EP - 151 PY - 2008 DA - 2008/05 SN - 5 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnam/803.html KW - finite element, finite volume element, second order hyperbolic equation, semidiscrete method, numerical quadrature, Ritz projection, optimal error estimates. AB -

We discuss a priori error estimates for a semidiscrete piecewise linear finite volume element (FVE) approximation to a second order wave equation in a two-dimensional convex polygonal domain. Since the domain is convex polygonal, a special attention has been paid to the limited regularity of the exact solution. Optimal error estimates in $L^2$, $H^1$ norms and quasi-optimal estimates in $L^∞$ norm are discussed without quadrature and also with numerical quadrature. Numerical results confirm the theoretical order of convergence.

S. Kumar, N. Nataraj & A. K. Pani. (1970). Finite Volume Element Method for Second Order Hyperbolic Equations. International Journal of Numerical Analysis and Modeling. 5 (1). 132-151. doi:
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