Finite Element Methods For Fourth Order Nonlinear Singular Parabolic Problems

The parabolic equations with singular coeffoients are very important ones in practical problems. Such as in nuclear physics, gas dynamics, mochanics, boundary layer theory, nonlinear filed and optics. The finite element method (FEM) is now a classical method for solving the partial differential equations arising in various contexts of science and technology. In recent years, many researchers have studied the partial differential equations with singular coefficients by finite difference method, symmetric finite element method, nonsymmetric finite element method and so on. Some ideal results have been obtained.In this article, a class of fourth order nonlinear boundary problems with singular coefficient is considered. First of all, existence and uniqueness of the weak solution of the variational problem is proved; Secondly, the weighted L₂ norm, the weighted H² norm error estimation for semi-discrete problems were obtained; Thind, error estimation in weighted L₂ norm for fully-discrete problems was obtained; At last , we give the posteriori error estimation with finite element semi-discrete methods for another nonlinear singular parabolic problem.