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Convergence analysis of a discontinuous Galerkin method for wave equations in second-order form. (English) Zbl 1450.65119

The paper studies the convergence of a spatial discontinuous Galerkin finite element method for the wave equation. An optimal energy error estimate is proved for shape regular and quasi-uniform meshes, which improves an existing suboptimal a priori error estimate. Moreover, a supercloseness result is established by adding a penalty term to the variational form. The superconvergence based on the polynomial preserving recovery for the modified scheme is proved. Numerical examples are included.

MSC:

65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
65M15 Error bounds for initial value and initial-boundary value problems involving PDEs
35B45 A priori estimates in context of PDEs
35L10 Second-order hyperbolic equations
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References:

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