The Best -Approximation Weighted-Residuals Method for Finite Element Approximations

In this article it is presented a Petrov-Galerkin method which gives a least-squares solution, useful for that problems for which the standard Galerkin method wildly oscillates and does not give an optimal approximation. The method proposed computes the weighting-functions that give the best-approximation in the norm induced by the inner product used to formulate the weighted residuals. We give an efficient implementation of this method using a space of linear finite elements.