Finite Volume Element Method for Second Order Hyperbolic Equations
Keywords:
finite element, finite volume element, second order hyperbolic equation, semidiscrete method, numerical quadrature, Ritz projection, optimal error estimates.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.