Finite Volume Element Method for Second Order Hyperbolic Equations

Kumar, S. ; Nataraj, N. ; Pani, A. K. (2008) Finite Volume Element Method for Second Order Hyperbolic Equations International Journal of Numerical Analysis and Modeling, 5 (1). pp. 132-151. ISSN 1705-5105

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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 quasioptimal estimates in L-infinity norm are discussed without quadrature and also with numerical quadrature. Numerical results confirm the theoretical order of convergence.

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