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Adaptive finite element methods for optimal control of second order hyperbolic equations. (English) Zbl 1283.35054

Summary: In this paper we consider a posteriori error estimates for space-time finite element discretizations for optimal control of hyperbolic partial dierential equations of second order. It is an extension of D. Meidner and B. Vexler [SIAM J. Control Optim. 46, No. 1, 116–142 (2007; Zbl 1149.65051)], where optimal control problems of parabolic equations are analyzed. The state equation is formulated as a first order system in time and a posteriori error estimates are derived separating the in uences of time, space, and control discretization. Using this information the accuracy of the solution is improved by local mesh refinement. Numerical examples are presented. Finally, we analyze the conservation of energy of the homogeneous wave equation with respect to dynamically in time changing spatial meshes.

MSC:

35L05 Wave equation
49J20 Existence theories for optimal control problems involving partial differential equations
65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
65M50 Mesh generation, refinement, and adaptive methods for the numerical solution of initial value and initial-boundary value problems involving PDEs

Citations:

Zbl 1149.65051
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