Mixed finite element method for a second order Dirichlet boundary control problem
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The main aim of this article is to analyze mixed finite element method for the second order Dirichlet boundary control problem. Therein, we develop both a priori and a posteriori error analysis using the energy space based approach. We obtain optimal order a priori error estimates in the energy norm and L^2-norm with the help of auxiliary problems. The reliability and the efficiency of proposed a posteriori error estimator is discussed using the Helmholtz decomposition. Numerical experiments are presented to confirm the theoretical findings.
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