Finite Volume Element Method For Elliptie Dirichlet Boundary Control Problems

Optimal control plays an important role in many engineering applications.Therefore,the numerical method of optimal control problem has attracted more and more interest from scholars.It is widely used in aerospace,bioengineering energy development,air pollution control and population,temperature control and other scientific and technology fields.From the point of view of mathe?matical research,the optimal control problem can often be transformed into the extremum problem of functional,but it is difficult to obtain the analytic solution of the control problem.The existing numerical methods mainly include finite element method,finite volume element method,finite difference method and spectral method.The finite volume element method(FVM)has attracted more and more attention because of its characteristics of maintaining local conserva-tion of physical quantities and simple numerical calculation format.In practical computing problems,we often encounter the optimal control problem with Dirichlet boundary.Because it is difficult to obtain the high-precision numerical scheme for the optimal control problem of elliptic partial differential equations with Dirichlet boundary constraints,there are few second-order precision schemes.How to obtain a high-precision format for a problem like this is a challenging task in scientific computing and engineering applica?tions.Innovation points of this paper is to use the finite volume element method to solve the rectangular area with Dirichlet boundary constraints on the optimal control problem of elliptic partial differential equation,with the method of opti-mized discrete first,use to pull a long day in the process of optimizing multiplier method to obtain optimality group,discrete nonlinear coupled systems using the finite volume element method,using quadratic interpolation overcomes the pro-jection equation with the directional derivative of reduced order of difficulty,make state,accompanying state,control have reached the second order accura-cy.Finally,numerical experiments are given to demonstrate the effectiveness of the proposed method.