Two Kinds Of Finite Element Method Calculations For Solving Korteweg-de Vries Equation

Over the years,the finite element method has embodied its feasibility and superiority in many fields.Especially in mathematics,It is widely used in the numerical solution of partial differential equations and has advantages with its unique characteristics.This article uses the space-time coupled finite element method and the space-time decoupled finite element method to calculate the numerical solution of the Korteweg-de Vries equationFirst of all,this paper takes the two-dimensional region formed by the time domain and space domain of the Korteweg-de Vries equation as the solution area,triangulates it.and completes the finite element solution process on this basis.Secondly,according to the characteristics of the initial value problem,We discrete time domain.Starting from the moment t0,the finite element method is used to solve each discrete time domain in turn to obtain the corresponding ODE.Then the finite element numerical calculation in the space domain is performed on the ODE to complete the entire numerical calculation.The above two methods use Picard iterative method to deal with nonlinear terms.This article analyzes and compares the two calculation results.The validity of the two finite element methods on the KdV equation is verified through numerical experiments...