Numerical Method For Groundwater Pollution Model Pollution Model And Maxwell's Equation

There are two mathematical problems in this paper, one of which is the groundwater pollution problem in aggregated porous media, and the other is Maxwell's Equation. The alternating-direction iterative technique is serviced for both mathematical problems, For groundwater pollution problem in ag-gregated porous media, a backward Euler-Galerkin method is applied, and an alternating-direction preconditioned iterative method with extrapolated along characteristics is used to solve the approximately discrete equations. Optimal order L2- error estimates are obtained under optimal estimate work and no damage to the precision. Moreover, high order accuracy with respect to time is obtained. For the static 2-D Maxwell's equation, an Arrow-Hurwitz iterative algorithm is concerned, and an experimental results is obtained to compare with the real and the numerical solutions of the mixed finite element method.An outline of the paper is as follow. The background of this paper is discribed in chapter 1, it just introduced the two problems, and the technique we will use. The models we will study in the next chapter are as follows, that is and the Maxwell equationsThere are three and four subsections in chapter 2 and chapter 3 separately. In§2.1, some results of the convection-dispersion problems are introduced, and pinpoint which model we will concern. Then, an alternating-direction pre-conditioned iteration algorithms, with backward Euler-Galerkin method along characteristics, is builded up in§2.2. And an error estimate obtained in§2.3 such asThe first of the third chapter described a history of the numerical methods about Maxwell's Equation, some of the classical methods are contained. Then, the next two parts described the mixed finite clement spaces we will use and builded up the approximates equations'Arrow-Hurwitz iteration form. In the end of this chapter is a numerical experimental about the problem shown in the early subsections, and the error estimate of the approximations are shown in the table:迭代次数And an analysis is obtained, that is:The more iterative, the more precise; and the Arrow-Hurwitz algorithm is better than the mixed finite element method, or at least.