Superconvergence for optimal control problems governed by semilinear parabolic equations

Abstract

In this paper, we first investigate optimal control problem for semilinear parabolic and introduce the standard $ L^2(\Omega) $-orthogonal projection and the elliptic projection. Then we present some necessary intermediate variables and their error estimates. At last, we derive the error estimates between the finite element solutions and $ L^2 $-orthogonal projection or the elliptic projection of the exact solutions.

Keywords

• finite element approximation
• semilinear parabolic equation
• optimal control problem
• the elliptic projection
• l²-orthogonal projection
• superconvergence