The Quadratic Finite Element Operator-splitting Method For High Dimensional With Parabolic Problem

Parabolic equation is an important partial differential equation.High dimensional parabolic equations have appeared in the fields of theoretical physics,finance,stochastic processes and many other fields.In order to meet the urgent needs of the times,this paper is devoted to solving the parabolic problems with high dimensions.The main innovation point is revising the addition of alternating direc-tion method into the product type alternating direction method.There are three main methods.The first approach simplifies the original ADI format.The second is to use the backward-euler scheme in the time direction,and the quadratic finite element in space.And the third adopts Crank-Nicolson method in time,and quadratic finite element in space.These three meth-ods not only improve accuracy but also enlarge computing scale.So far,10 dimensional parabolic equation has been solved.This is a new research that uses stack accumulation spectral method to solve higher dimensional problems.