INTERPOLATED FINITE ELEMENT METHOD FOR SOME FOURTH-ORDER ELLIPTIC PROBLEMS

We introduce nonstandard interpolated finite elements providing better accuracy for a fourth-order elliptic boundary value problems, as well as to the biharmonic eigenvalue problems. The term "ultraconvergence" indicates that the convergence rate is at least two orders higher than the optimal global rate. This method is a variant of a postprocessing procedure when the known finite element solution is used. Moreover, a posteriori error estimates of global ultraconvergent type are derived. The presented approach is applicable for the general rectangular finite element meshes. Some numerical results illustrate the efficiency of the proposed algorithm.