Finite Volume Element Study Of Semilinear Parabolic Problems

Aiming at the problem of solving a class of semilinear parabolic differential equations,the semi-linear terms are processed by interpolation.The calculation format and convergence of the finite volume element method for interpolation coefficients of the fixed-solution problem are studied.For the one-dimensional semilinear parabolic problem,first of all,the interpolation coefficient finite volume element is applied to semi-discretization in space,and the forward difference method and backward difference method are used to completely discretize the interpolation coefficient finite volume element in space,respectively,and the backward difference method is used to fully discretize the interpolation coefficient finite volume element.Then the convergence of the scheme is discussed and two numerical examples are given to illustrate the effectiveness of the scheme.Similarly,for the quadratic element,the interpolation coefficient finite volume element is used for semi-discretization in space,and the Runge-Kutta method is used to obtain the fully discrete computational scheme in time.Then the convergence of the scheme is discussed.Finally,a numerical example is given.For the fixed solution problem of two-dimensional semilinear parabolic differential equations,the spatial semi-discretization based on triangulation and the corresponding time-fully discrete computational schemes and algorithms are also discussed in this paper.