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

Preview Full PDF 573 2231
Export citation
  • 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 quasioptimal estimates in L-infinity 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

  • Email address
  • BibTex
  • RIS
  • 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 quasioptimal estimates in L-infinity 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 KW - finite volume element KW - second order hyperbolic equation KW - semidiscrete method KW - numerical quadrature KW - Ritz projection KW - 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 quasioptimal estimates in L-infinity 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:
Copy to clipboard
The citation has been copied to your clipboard