A Weak Galerkin Finite Element Method For Fourth Order Parabolic Partial Differential Equations

This paper is concerned with a weak Galerkin finite element method for the forth or-der parabolic equation.At the beginning,based on the variational formulation of elliptic equations in an arbitrary polygon or polyhedral region,the appropriate weak function space is defined.The weak differential operators are introduced to replace the classical differ-ential operators in the variational formulation to obtain a new numerical format.The weak differential operators defined here apply to both continuous functions and completely discon-tinuous functions.This is an important complement to the finite element methods of fourth order equations.By using the framework of Galerkin methods,the uniqueness of the solu-tion is ensured and the error estimates are obtained by introducing an appropriately defined stabilizer.Finally,the convergence error estimates for the half-discrete and fully discrete finite element schemes in L2 as well as the discrete H2 with respect to the spatial variable are presented,respectively.The numerical experiments are given to verify corresponding theoretical analysis.