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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} }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.