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Keywords:

  • a priori error estimates;
  • optimal control problems;
  • hyperbolic integrodifferential equations;
  • semidiscrete expanded mixed finite element methods

Abstract

In this article, we investigate the L(L2) -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