Adaptive characteristic finite element approximation of convection–diffusion optimal control problems. Issue 3 (30th July 2012)

• Record Type: Journal Article
• Authors: Fu, Hongfei; Rui, Hongxing
• Is Part Of: Numerical methods for partial differential equations. Volume 29:Issue 3(2013:May)
• Page Start: 979
• Page End: 998
• Publication Date: 2012-07-30
• Subjects: Differential equations, Partial -- Numerical solutions -- Periodicals; 515.353
• DOI: 10.1002/num.21741
• Languages: English
• ISSNs: 0749-159X

Abstract

<abstract abstract-type="main" xml:lang="en"> <title>Abstract</title> <p>In this article, a characteristic finite element approximation of quadratic optimal control problems governed by linear convection–diffusion equations is given. We derive some a posteriori error estimates for both the control and the state approximations, where the control variable is constrained by pointwise inequality. The derived error estimators are then used as an error indicator to guide the mesh refinement. In this sense, they are very important in developing adaptive finite element algorithm for the optimal control problems. Finally, a numerical example is given to validate the efficiency and reliability of the theoretical results. © 2012 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2013</p> </abstract>