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Conjugate gradient-boundary element solution using multiple reciprocity method for distributed elliptic optimal control problems. (English) Zbl 1149.49029

Summary: This paper deals with the numerical solution of optimal control problems, where the state equations are given by the fourth order elliptic partial differential equations. An iterative algorithm for this class of problems is developed. This new proposal is obtained by combining the conjugate gradient method with the boundary element method and multiple reciprocity method. The local error estimates based on the stability of this scheme in the \(H^{2}\) norm, \(L^{2}\) norm and \(L^{\infty }\) norm are obtained. Finally, the numerical results on a test case show that this method is correct and feasible.

MSC:

49M30 Other numerical methods in calculus of variations (MSC2010)
65N38 Boundary element methods for boundary value problems involving PDEs
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
65N35 Spectral, collocation and related methods for boundary value problems involving PDEs
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