Analysis and approximation of optimal control problems for first-order elliptic systems in three dimensions

DOI10.1016/S0096-3003(98)00017-4zbMath0928.49023MaRDI QIDQ1294280

Hyung-Chun Lee, Max D. Gunzburger

Publication date: 15 December 1999

Published in: Applied Mathematics and Computation (Search for Journal in Brave)

zbMATH Keywords

finite elementselliptic systemssteady state optimal control problems

Mathematics Subject Classification ID

Optimality conditions for problems involving partial differential equations (49K20) Newton-type methods (49M15) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Existence theories for optimal control problems involving partial differential equations (49J20)

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A least-squares method for optimal control problems for a second-order elliptic system in two dimensions, Least-squares finite-element methods for optimization and control problems for the Stokes equations, Optimal control approach to data set alignment, Formulation and multigrid solution of Cauchy-Riemann optimal control problems, Construction of differentiable transformations, A least-squares/penalty method for distributed optimal control problems for Stokes equations, A full multigrid solution of control-constrained Cauchy–Riemann optimal control problems, A penalty/least-squares method for optimal control problems for first-order elliptic systems

Cites Work

• A finite element method for first order elliptic systems in three dimensions
• A theorem about the complete set of isomorphisms for systems elliptic in the sense of Douglis and Nirenberg
• Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions II
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