Superconvergence of $H$1-Galerkin Mixed Finite Element Methods for Elliptic Optimal Control Problems

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Abstract

The convergence of $H$1-Galerkin mixed finite element methods for elliptic optimal control problems is studied and postprocessing operators are used to establish the superconvergence for control, state and adjoint state variables. A numerical example confirms the validity of theoretical results.

Keywords:

Elliptic equations optimal control problems superconvergence $H^1$-Galerkin mixed finite element methods.
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DOI

10.4208/eajam.150117.070618