On finite element method of high-order accuracy for two-point degenerated Dirichlet problem of 4th order

In this paper two-point boundary value problem for a differential equation of 4th order with degeneration is considered. This problem is solved by the finite element method of high-order accuracy with a multiplicative separation of singularity. The optimal convergence rate of the presented method for a given class of smoothness of the right-hand sides is proved.