ISSN:
1573-2878
Keywords:
Heat equation
;
boundary control problems
;
adjoint equations
;
Hilbert uniqueness method
;
regularization
;
penalty
;
convex duality
;
variational inequalities
;
conjugate gradient methods
;
finite difference methods
;
finite element methods
;
operator splitting algorithms
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract The present article is concerned with the numerical implementation of the Hilbert uniqueness method for solving exact and approximate boundary controllability problems for the heat equation. Using convex duality, we reduce the solution of the boundary control problems to the solution of identification problems for the initial data of an adjoint heat equation. To solve these identification problems, we use a combination of finite difference methods for the time discretization, finite element methods for the space discretization, and of conjugate gradient and operator splitting methods for the iterative solution of the discrete control problems. We apply then the above methodology to the solution of exact and approximate boundary controllability test problems in two space dimensions. The numerical results validate the methods discussed in this article and clearly show the computational advantage of using second-order accurate time discretization methods to approximate the control problems.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF02192213
Permalink
