Volume 4, Issue 3-4
Discontinuous Galerkin Approximations for Distributed Optimal Control Problems Constrained by Parabolic PDE's

V. J. Ervin and W. J. Layton & M. Neda

Int. J. Numer. Anal. Mod., 4 (2007), pp. 690-712

Preview Full PDF BiBTex 0 397
  • Abstract

A discontinuous Galerkin finite element method for optimal control problems having states constrained by linear parabolic PDEs is examined. The spacial operator may depend on time and need not be self-adjoint. The schemes considered here are discontinuous in time but conforming in space. Fully-discrete error estimates of arbitrary order are presented and various constants are tracked. In particular, the estimates are valid for small values of alpha, gamma , where alpha denotes the penalty parameter of the cost functional and gamma the coercivity constant. Finally, error estimates for the convection dominated convection-diffusion equation are presented, based on a Lagrangian moving mesh approach.

  • History

Published online: 2007-04

  • AMS Subject Headings

65M60, 49M25, 65M12

  • Cited by