fuzzy partition; standard BVP; F-transform;Galerkin method

The aim of the contribution is to propose and justify a new methodology in the construction of spaces of test functions used in a weak formulation of the Boundary Value Problem. The construction is based on a fuzzy partition of the problem domain and selected test functions are connected with the construction of higher degree F-(fuzzy) transform components. The main advantage of this so called ``two dimensional'' approach consists in the independent selection of the key parameters, aiming at achieving a requested quality of approximation with a reasonable complexity. We give theoretical justification and illustration on examples that confirm our methodology.