Finite Element Methods For Fourth Order Singular Nonlinear Boundary Value Problem In One Dimension

The partial differential equations with singular coefficients are very important ones in the field of numerical mathematics. Many researchers have kept their eyes on all sorts of numerical methods and the corresponding mathematical theories to solve them early from 1960s. In this article, a class of nonlinear elliptic boundary value problems with singular coefficient in one-dimensional domain was considered.first of all existence and uniqueness of the weak solution of the variational problem corresponding to the originalequation ,is proved . secondly, l2 and uniform norm error estimates for theGalerkinapproximation of the under-considered problem via a comparison with theE-norm projection of the solution are obtained.