A priori error estimates and superconvergence of P02-P1 mixed finite element methods for elliptic boundary control problems
Ch. Xu
Beihua University, Jilin, China
Keywords: elliptic equations, boundary control problems, a priori error estimates, superconvergence, P-P mixed finite element methods
Abstract
In this paper, we discuss a priori error estimates and superconvergence of P 02- P 1 mixed finite element methods for elliptic boundary control problems. The state variables and co-state variables are approximated by a P 02- P 1 (velocity-pressure) pair and the control variable is approximated by piecewise constant functions. First, we derive a priori error estimates for the control variable, the state variables and the co-state variables. Then we obtain a superconvergence result for the control variable by using postprocessing projection operator.
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