The Numerical Solution Of Two Dimensional Variable Coefficients Elliptic Equations And Calculating Inversion Parameters

Many problems in the nature science and engineering technology fields can be described by partial differential equations. So it is a powerful tool for handling the problems to investigate the numerical solution of the equations. As for a special area of research, it has been attracting many researchers' concentrations on it. And many latest researches have been taken into practical applications. In this paper, the Finite Difference Method (FDM) and Finite Element Method (FEM) are adopted to solve a two-dimensional variable coefficient ellipse equation with boundary conditions; the corresponding error estimation is derived. Numerical simulations presented show that the FEM has advantages of high accuracy and simplicity in programming.If the operator, the right term, the boundary condition or the initial conditions is unknown, meanwhile, the solution of the equation is unknown either; this makes an inverse problem of the partial differential equation. So it gets more challenging compared with the direct one, with its nonlinearity and ill-pose considered. And it becomes a new research field attracting more and more researchers working on it.Inverse problem of mathematics physical equation is an interdisciplinary and frontier science. It has great significance not only in theory but also in practice. In this paper a systematic research is made on the theory, solution, analytical approach and engineering application of the inverse problem of a two-dimensional variable coefficient ellipse partial differential equation.In this paper, the parameter inversion of two-dimensional convection-diffusion equation is investigated using the iterative method, and its numerical solution is derived. The results of numerical simulation show that the iterative method is effective and feasible. Also, additional investigation on inverse problem in identification of the steady-state permeability for two-dimensional isotropic medium using genetic algorithm is given. At last, many numerical simulations illustrate that, the method adopted in this paper has good stability and highaccuracy in solving the complex inverse problems.