Collocation finite element and spectral methods for one dimensional biharmonic equations

This article is concerned with collocation-finite element and collocation-spectral methods with piecewise and orthogonal polynomials to numerically solve one dimensional biharmonic equations. We considered a general formula for the B-splines of kth degree, error analysis is also given. Variational inequality approach is used to prove the existence and uniqueness of the solution. Comparison is made between different methods.