ABSTRACT
The importance of conservation laws is well known. Recently, practical requirements have stimulated the construction of modified variational principles and the development of dual variational methods for the solution of elliptic boundary value problems. In the numerical realisation of dual methods, both the direct (original) extremal problem and its dual are solved. After obtaining approximate solutions by means of the corresponding direct and dual variational formulations, we can determine both upper and lower estimates for the exact value of the extremal of the original problem, and a posteriori energy estimate for the accuracy of the approximate solution.
