EQUIVALENT A POSTERIORI ERROR ESTIMATES FOR A CONSTRAINED OPTIMAL CONTROL PROBLEM GOVERNED BY PARABOLIC EQUATIONS

作者：Sun, Tongjun^*; Ge, Liang; Liu, Wenbin

来源：International Journal of Numerical Analysis and Modeling, 2013, 10(1): 1-23.

• constrained optimal control problem
• adaptive finite element approximation
• equivalent a posteriori error estimates
• parabolic equations
• multi-meshes

In this paper, we study adaptive finite element approximation in the backward Euler scheme for a constrained optimal control problem by parabolic equations on multi-meshes. The control constraint is given in an integral sense: K = {u(t) is an element of L-2(Omega) : a <= integral(Omega) u(t) <= b}. We derive equivalent a posteriori error estimates with lower and upper bounds for both the state and the control approximation, which are used as indicators in adaptive multi-meshes finite element scheme. The error estimates are then implemented and tested with promising numerical experiments.

• 出版日期2013
• 单位山东大学