Galerkin finite element procedure - a worked example

2 Galerkin finite element procedure - a worked example 

Within the space of finite elements the unknown function is approximated using shape functions corresponding to the two-noded (linear) Lagrange elements as 

The residual obtained via the insertion of t into the differential equation is weighted and integrated over each element as 

At this stage the fonnulated Galerkin-weighted residual Equation (2.52) contains second-order derivatives. Therefore elements cannot generate an acceptable solution for this equation (using C elements the first derivative of 

46 WEIGHTED RESIDUAL FINITE ELEMENT METHODS - AN OUTLINE 

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