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Finite element approximation of the acoustic wave equation: Error control and mesh adaptation. (English) Zbl 0948.65098
The authors use an adaptive finite element method to solve the acoustic wave equation. They find an a posteriori error estimate of a linear functional of the solution by solving numerically a dual problem and use this estimate to refine the mesh locally and so increase the efficiency of the method. Numerical examples illustrate the method.

MSC:
65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
65M15 Error bounds for initial value and initial-boundary value problems involving PDEs
35L15 Initial value problems for second-order hyperbolic equations
Software:
deal.ii
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