SIAM Journal on Control and Optimization · 1990 · 117 citations · 5 references
Natural SciencesMathematicsComputational Fluid DynamicsComputational MechanicsDifferential EquationsConvergence AnalysisError EstimationParameter EstimationPartial Differential EquationsWeak FormulationCoercivityConvergenceElliptic Partial Differential EquationsError Estimation For Nonlinear ProblemsLagrangian FormulationParameter Identification In Lagrangian SystemsRegularizationRegularization Techniques
In this paper a new technique for the estimation of parameters in elliptic partial differential equations is developed. It is a hybrid method combining the output-least-squares and the equation error method. The new method is realized by an augmented Lagrangian formulation, and convergence as well as rate of convergence proofs are provided. Technically the critical step is the verification of a coercivity estimate of an appropriately defined Lagrangian functional. To obtain this coercivity estimate a seminorm regularization technique is used.
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