Weak Galerkin Finite Element Methods For The Biharmonic Equation

In recent years, with the wide application of biharmonic equation, aimming at the research of these equations has become a new hot spot in the research field of the d-ifferential equation, simultaneously, the finite element method of these equations has also become the core issue of the research field, moreover, it has become an important content of study Topic.Aimming at the characteristics of these kinds of equations, this article greatly re-duces the difficulty of the numerical solution of biharmonic equation by adopting weak Galerkin finite element methods; meanwhile, through the research of the existence, u-niqueness and convergence of the solution of biharmonic equation, it has been proved that the method is very effective and stable, the result shows that weak Galerkin finite element methods is superior.The organisation of the article is as follows:1. The first chapter introduces the background and the development of the bihar-monic equations.2. In the second chapter,we will introduce some basic throrems and definitions.3. In the third chapter,we will introduce the weak Galerkin finite element methods methods.4. In the forth chapter.the convergence and error estimates of the algorithm is estab-lished for the WG-FEM solutions.5. In the fifth chapter,we will present some numerical experiments to confirm the theory of convergence and error is correct.