A New Characteristic Mixed Element Method For Saltwater Intrusion Problem

As we know,the seawater intrusion problem attracts great attentions recently since it causes great damages to industrial and agricultural production.It refers to the complex movement of seawater intrusion into the groundwater aquifers,which is generally caused by economic development and the change of natural water environment.This will bring serious harm to the human life and economic development of the coastal areas.At present,dozens of countries and regions around the world have discovered the problem of seawater intrusion.Therefore,this problem has been widely concerned by the international community Many countries are actively carrying out research and management of seawater intrusionThe mathematical model of seawater intrusion is composed of the water head equation and the concentration equation.In this paper,we study a new splitting characteristic mixed algorithm for seawater intrusion.First,we review the splitting positive mixed finite element method and the mass-conservative characteristic method.Then,the two methods are used to deal with the actual problems of seawater intrusion.After that,this method is further extended to the incompressible miscible displacement in the porous mediaThe main contents are as followsFirst,in the second chapter,we use the splitting positive definite mixed finite element method to establish a time two order splitting mixed finite element method for solving the parabolic equation.The corresponding theoretical analysis and the prior error estimation are given.At the same time,numerical experiments prove the feasibility and efficiency of splitting positive definite mixed finite element,and the accuracy of the priori error estimation.In addition,this method extends the application of the molecular chemotaxis modelSecond,in the third chapter,a new mass-conservative characteristic algorithm is established to solve the convection-dominant Sobolev equation.In this algorithm,we use the mass-conservative characteristic method to deal with the convection term and combine the splitting positive definite mixed finite element method.We give a priori error estimation for the finite element method,and give the corresponding numerical experiments and analyze the experimental resultsThird,in the fourth chapter,we consider the combination of the splitting positive mixed finite element method and mass-conservative characteristic method to solve the problem of seawater intrusion.The corresponding theoretical analysis and the prior error estimation are givenFinally,In the fifth chapter,we use the MCC-Hybrid mixed element method to deal with incompressible miscible displacement problem,and construct the corresponding numerical schemes,and give corresponding theoretical analysis and priori error estimates.