O pewnej interpretacji metod energetycznych dla problemów filtracji ustalonej

Analysed boundary value problem for steady seepage is described by partial differential equation (1) with boundary conditions (2) and (3) or by energy functional (5) with boundary conditions (2). The weighted squared error of velocity components (7) is assumed as the error measure of an approximate solution to the problem. It is proved that the minimization of the weighted squared error over whole flow domain (8) is equivalent to the corresponding variational formulation (5). Thus, variational methods for steady seepage problems may be interpreted as the least squared error procedure where the measure of error is the weighted function of the errors in the velocity components. The formulation of variational methods as a minimum least squared error procedure is susceptible to interpretation of some properties of the obtained solutions and affords a method of convergence. These aspects have been discussed for the finite elements method.