Weak Galerkin Finite Element Method For The Hyperbolic Equation

In this dissertation we mainly research the weak finite element method for the hyperbolic equation.We use the implicit Euler method to discrete in time for the hyperbolic equation,and the weak finite element method is used in space.Then we obtained the fully discrete scheme of the equation.In this paper,we also give the stability and convergence of the fully discrete scheme.Two numerical examples are used to confirm our theoretical results.The order of space convergence can reach k + 1,and the time order can reach the second order.In this paper,chapter 1 and chapter 2 introduce the research-ing background and current situation of hyperbolic equation,and the related knowledge and lemmas of the weak finite element.Chap-ter 3 gives the full discrete scheme of the hyperbolic equation.Chapter 4 mainly proves the stability and convergence of the dis-crete scheme.Chapter 5 proves the theoretical results through numerical examples.Chapter 6 is the summary and prospect of this paper.