Continuous Space-Time Finite Element Method For Semilinear Singular Parabolic Equation

Singular differential equations arise from some practical problems of physics and enginerring,it is important to analyse and solve numerially this kind of equations.Many methods, including difference methods,collocation methods and standard finite element methods for singular parabolic equations have been proposed and analyzed ,and some good results have been obtained. In this paper a new variational method for approximating the semilinear singular parabolic equation is given by using continuous finite elements in space and time .In contrast to the methods mentioned above, we use finite elements to discretize in space and time simulaneously.In the two directions of space and time higher accuracy is achieved.The proof of existence of the finite element solutions and their theoretical error estimates are presented.