Discontinuous Finite Element Method For Differential Equations With Periodic Initial Conditions

Discontinuous finite element method is used to completely discontinuous piecewise polynomial space as the solution space and the test function space is a kind of finite element method,the research theme of superconvergence of discontinuous finite element method for solving partial differential equations in recent years is also the scholars interested in.In this paper,we study the discontinuous finite element method for a class of differential equations with periodic initial conditions and its convergence properties.In this paper,we study the first order hyperbolic equation and parabolic equation with periodic initial conditions.For the first order hyperbolic equation in general,the mixed bound-ary problem of its equivalent transformation with periodic boundary condition,finite element method was researched from corresponding upwind numerical flow,structural correction function to obtain superapproximation finite element interpolation function,we prove a discontinuous finite element and discontinuous finite element at any point error and the range of the average error estimate;second order 4 Runge-Kutta a finite element time fully discrete scheme and full discrete backward calculation format,two fully discrete finite element calculation formulae;the first two numerical examples are given to verify the validity of the calculation method.For the solutions of parabolic equations in general,introduces local discontinuous element method,and deduces a dimensional time fully discrete scheme and full discrete backward calculation format;4 order Runge-Kutta two fully discrete finite element scheme.