A novel local representation for the unknown functions and the corresponding derivative quantities of interest, which contains "built in" the information from the field equations, is presented. It can be used in connection with element (by element) or patch (by patch) recovery procedures. A patch recovery technique, which uses this local representat ion to get improved global, C^O-continuous, smoothed finite element approximations for the derivative quantities (such as gradient components or strains) from the results of standard finite element analysis, is developed. The presented local representation is considered in more detail in connection with the so called quasi-harmonic equation and the plane elasticity problem. Two numerical examples with experimental convergence study of the energy norm are finally given.

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