Discontinuous Galerkin time stepping methods for second order hyperbolic problems
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Discontinuous Galerkin methods, based on piecewise polynomials of degree q≥ 0, are investigated for temporal semi-discretization for second order hyperbolic equations. Energy identities and stability estimates of the discrete problem are proved for a slightly more general problem, that are used to prove optimal order a priori error estimates with minimal regularity requirement. Uniform norm in time error estimates are proved for the constant and linear cases. Numerical experiments are performed to verify the theoretical rate of convergence.
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