The Linear Finite Element Model Of BBM-Burgers Equation Based On Moving Mesh

In this thesis,we proposed a linear finite element model to solve the BBM-Burgers equation,the model is based on an adaptive moving mesh.This model can be applied to a series of nonlinear partial differential equations with spatial-time mixed derivatives,we also make use of the model to simulate the BBM-Burgers equation with high-order dissipative term,we discuss the dissipation effect of dissipative term and analyse the effect of the rate of numerical solutions' decay the dissipative term's coefficients caused.To make use of the moving mesh linear finite element model discreting the BBM-Burgers equation,we need to introduce new variables to replace the spatial-time mixed derivatives,because the mixed derivatives can not be defined on moving mesh,the changed equation becomes into a coupled system.In the model,the finite element method based on moving mesh is used to discrete the spatial derivatives,the fifth-order Radau IIA method is used to discrete the time derivatives.In this paper,in order to verify the superiority of the finite element model based on moving mesh,a large number of numerical examples show the differences between moving mesh finite element method and fixed mesh finite element method,the experimental results show us that when the element number is same,the error of moving mesh is much less than that of fixed mesh and all the two methods can reach the same convergence order.Comparing the moving mesh model with the fixed mesh model,we find the moving mesh model can simulate the real phenomenon more accurately.By numerical simulations of the one-dimensional BBM-Burgers equation with a fourth-order dissipative term,we find the dissipative term uxx plays a more important role than uxxxx in dissipation.When there exist two same BBM equations with different dissipative terms and maximum value Umax of the numerical solutions is same at the final time,the coefficient of uxxxx is around 50 times that of uxx in the same BBM cquation with different,dissipativc terms in respect of dissipation.