Abstract
In this article, we study the Dirichlet boundary control problem governed by Poisson equation, therein the control is penalized in H1(Ω) space and various symmetric discontinuous Galerkin finite element methods are designed and analyzed for its numerical approximation. Symmetric property of the bilinear forms is exploited to obtain the discrete optimality system. By a careful use of various intermediate problems, the optimal order convergence rates are obtained for the control in the energy and L2-norms. Moreover, using an auxiliary system of equations, a posteriori error estimator is derived which is shown to be reliable and efficient. Numerical experiment results are included to confirm the theoretical findings.
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