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 - <p style="text-align: justify;">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.</p>