Galerkin weighted residual statement

Following the discretization of the solution domain Q (i.e. line AB) into two-node Lagrange elements, and representation of T as T = Ni(x)Ti) in terms of shape functions A, (.v), i = 1,2 within the space of a finite element Q, the elemental Galerkin-weighted residual statement of the differential equation is written as... 

Following the procedure described in Chapter 3, Section 1.1 the Galerkin-weighted residual statements corresponding to Equations (4.4) and (4.1) are written as... 

In the standard Galerkin method (also called the Bubnov-Galerkin method) weight functions in the weighted residual statements are selected to be identical... 

In order to reduce the continuity requirements of the trial functions f, usually the weaker residual statement (2.8) is used and although not necessary, the weight functions are taken equal to the trial functions (Galerkin s method producing a symmetric matrix) to obtain... 

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