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A posteriori error estimates of triangular mixed finite element methods for semilinear optimal control problems. (English) Zbl 1262.49009
Summary: In this paper, we present an a posteriori error estimates of semilinear quadratic constrained optimal control problems using triangular mixed finite element methods. The state and co-state are approximated by the order $$k\leq 1$$ Raviart-Thomas mixed finite element spaces and the control is approximated by piecewise constant element. We derive a posteriori error estimates for the coupled state and control approximations. A numerical example is presented in confirmation of the theory.

##### MSC:
 49J20 Existence theories for optimal control problems involving partial differential equations 65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
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