Superconvergence and L-infinity-Error Estimates of the Lowest Order Mixed Methods for Distributed Optimal Control Problems Governed by Semilinear Elliptic Equations

作者：Hou; Tianliang

来源：Numerical Mathematics: Theory, Methods and Applications , 2013, 6(3): 479-498.

DOI：10.4208/nmtma.2013.1133nm

• Semilinear elliptic equations
• distributed optimal control problems
• superconvergence
• L-infinity-error estimates
• mixed finite element methods

In this paper, we investigate the superconvergence property and the L-infinity-error estimates of mixed finite element methods for a semilinear elliptic control problem. The state and co-state are approximated by the lowest order Raviart-Thomas mixed finite element spaces and the control variable is approximated by piecewise constant functions. We derive some superconvergence results for the control variable. Moreover, we derive L-infinity-error estimates both for the control variable and the state variables. Finally, a numerical example is given to demonstrate the theoretical results.

• 出版日期2013-8
• 单位华南师范大学