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Summary:
Dual variational principles for an elliptic partial differential equation of the second order with combined boundary conditions are formulated. A posteriori error estimates are obtained and for some class of problems the convergence of approximate solutions of the dual problem is proved. A numerical example is presented.
The analysis of the approximate solutions suggests that especially when we are interested mainly in the values of co-normal derivatives on the boundary the dual method can serve an effective method for a approximate solution.
References:
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