Approximation of the solution of a fourth order boundary value problem with nonsmooth coefficient

A class of generalized finite element methods for the approximate solution of fourth order two point boundary value problem with nonsmooth coefficient is presented. The methods are based on the use of problem dependent L-splines incorporating the nonsmoothness of the coefficient. Stability is proved and optimal error estimates in the H² norm are derived for the solution and postprocessed solution, under the assumption that the coefficient is of bounded variation. The relation of these methods to mixed methods is discussed.