Error estimates of expanded mixed methods for optimal control problems governed by hyperbolic integro‐differential equations. Issue 5 (14th February 2013)

• Record Type: Journal Article
• Authors: Hou, Tianliang
• Is Part Of: Numerical methods for partial differential equations. Volume 29:Issue 5(2013:Sep.)
• Page Start: 1675
• Page End: 1693
• Publication Date: 2013-02-14
• Subjects: Differential equations, Partial -- Numerical solutions -- Periodicals; 515.353
• DOI: 10.1002/num.21771
• Languages: English
• ISSNs: 0749-159X

Abstract

<abstract abstract-type="main" xml:lang="en"> <title>Abstract</title> <p>In this article, we investigate the <italic>L</italic>^{<italic>∞</italic>}(<italic>L</italic>²) ‐error estimates of the semidiscrete expanded mixed finite element methods for quadratic optimal control problems governed by hyperbolic integrodifferential equations. The state and the costate are discretized by the order <italic>k</italic> Raviart‐Thomas mixed finite element spaces, and the control is approximated by piecewise polynomials of order <italic>k</italic>(<italic>k</italic> ≥ 0). We derive error estimates for both the state and the control approximation. Numerical experiments are presented to test the theoretical results. © 2013 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2013</p> </abstract>