Finite Volume Element Method For Dissipative SRLW Equations

In this paper, the finite volume element method is analyzed for the dissipative sym-metric regularized long wave equation. The theoretical analyses and numerical simulations are given.In Chapter 1, we briefly introduce the background and the development of the dissi-pative symmetric regularized long wave equation.In Chapter 2, the semi-discrete scheme in space and fully discrete finite element scheme for the dissipative symmetric regularized long wave equations are constructed. the thought of this chapter:semi-discrete finite volume element scheme is derived, by doing subdivision of regions and constructing interpolation operator. Then, fully discrete finite volume element scheme is derived, by using the time back of discrete, the stability of numerical solution is analyzed and the optimal order error estimates of the numerical scheme are proved.In Chapter 3, fully discrete finite volume element scheme with second order accuracy in time are given, the stability of numerical solution is analyzed, the optimal order error estimates of the numerical scheme are proved.Finally, numerical examples are given to demonstrate the feasibility and effectiveness.