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Error estimates of expanded mixed methods for optimal control problems governed by hyperbolic integro‐differential equations
Author(s) -
Hou Tianliang
Publication year - 2013
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.21771
Subject(s) - mathematics , piecewise , finite element method , discretization , hyperbolic partial differential equation , quadratic equation , partial differential equation , optimal control , mathematical analysis , mathematical optimization , geometry , physics , thermodynamics
In this article, we investigate the L ∞ ( L 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 k Raviart‐Thomas mixed finite element spaces, and the control is approximated by piecewise polynomials of order k ( k ≥ 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