A Class Of Mixed Element Algorithm For Hyperbolic Burgers Equation

In this thesis,the H1-Galerkin mixed element algorithm is developed to solve a hyperbolic Burgers equation.By the introduction of an auxiliary variable,the previous problem can be changed into a lower coupled integro-differential system by solving an ordinary differential equation(ODE),and then the mixed weak formulation,semi-discrete scheme and two fully discrete schemes including Crank-Nicolson scheme and second-order backward difference system are given and some theoretical results and numerical results are provided.In chapter 2,the semi-discrete scheme in space is studied.First,with the auxiliary variable q = a(x)ux + b(x)uxt,the function ux is solved by the solving method of ODE,then the previous equation can be reduced into a coupled integro-differential system with lower derivatives,and the error estimates based on the semi-discrete H1-Galerkin mixed element method are done.In chapter 3,both Crank-Nicolson scheme and second-order backward difference scheme are formulated.Fully discrete error analysis based on two fully discrete scheme are considered and optimal error estimates in L2 and H1-norms are derived.In chapter 4,By choosing the simple numerical example,numerical errors and con-vergence results are shown to test the feasibility and effectiveness.