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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.

  • Keywords

finite element, finite volume element, second order hyperbolic equation, semidiscrete method, numerical quadrature, Ritz projection, optimal error estimates.

  • AMS Subject Headings

65N30, 65N15

  • Copyright

COPYRIGHT: © Global Science Press

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  • TXT
@Article{IJNAM-5-132, author = {S. Kumar, N. Nataraj and A. K. Pani}, 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 AU - S. Kumar, N. Nataraj & A. K. Pani 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 and A. K. Pani. (2008). 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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