Geodesic
Dual variational principles for an elliptic partial differential equation
Applications of Mathematics, Tome 21 (1976) no. 1, pp. 5-27

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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.
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.
DOI : 10.21136/AM.1976.103619
Classification : 35B45, 35J20, 65M99, 65N30 
Vacek, Jiří. Dual variational principles for an elliptic partial differential equation. Applications of Mathematics, Tome 21 (1976) no. 1, pp. 5-27. doi: 10.21136/AM.1976.103619
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