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A priori estimates for mixed finite element methods for the wave equation. (English) Zbl 0724.65087
The 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.

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
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