拋物型最優(yōu)控制問題有限元方法的超收斂性.pdf

1、湘潭大學(xué)碩士學(xué)位論文拋物型最優(yōu)控制問題有限元方法的超收斂性姓名：鄒衍華申請(qǐng)學(xué)位級(jí)別：碩士專業(yè)：計(jì)算數(shù)學(xué)指導(dǎo)教師：陳艷萍20080508ABSTRACTOptimal control problems are very important to many engineering applica-tions. For the last decades, it has become a very active and successful r

2、esearcharea. It is obvious that efficient numerical methods are very essential to success-ful solving the optimal control problems. Finite element approximation methodplays an very important role in solving the optimal c

3、ontrol problems.In this paper, we will investigate the superconvergence for the finite elementapproximation of quadratic optimal control problem governed by linear parabolicequation. The state and co-state are approximat

4、ed by the piecewise linear func-tions and the control is approximated by piecewise constant functions. We willconstruct the approximation schemes for the model optimal control problem, thenwe will introduce some intermed

5、iate and get its error estimates, by using the re-sults, we present the superconvergence analysis for both the control variables andthe state variables.Keyword: finite element approximation, superconvergence, paraboliceq