A priori estimates for mixed finite element methods for the wave equation.

*(English)*Zbl 0724.65087The authors analyze properties of mixed finite elements for hyperbolic equations; their paper studies mixed elements of two kinds, namely continuous and discrete in time; in the latter case, it is dealt with a parametric family with respect to time-step, ranging from the fully explicit version to the fully implicit one. A convergence result is proven with a priori error bounds for the continuous case, by reducing it to convergence properties of finite elements for elliptic equations. Stability is discussed for the discrete versions and a result is proven for the fully explicit one. Further results on stability for the other versions should appear in a forthcoming paper by the same authors. A final section with a wealth of numerical examples is included.

Reviewer: J.P.Milaszewicz (Buenos Aires)

##### MSC:

65M15 | Error bounds for initial value and initial-boundary value problems involving PDEs |

65M06 | Finite difference methods for initial value and initial-boundary value problems involving PDEs |

65M60 | Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs |

65M12 | Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs |

35L05 | Wave equation |

##### Keywords:

wave equation; mixed finite elements; hyperbolic equations; convergence; error bounds; Stability; numerical examples
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\textit{L. C. Cowsar} et al., Comput. Methods Appl. Mech. Eng. 82, No. 1--3, 205--222 (1990; Zbl 0724.65087)

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