Approximation of sparse controls in semilinear equations by piecewise linear functions
نویسندگان
چکیده
Abstract. Semilinear elliptic optimal control problems involving the L1 norm of the control in the objective are considered. A priori finite element error estimates for piecewise linear discretizations for the control and the state are proved. These are obtained by a new technique based on an appropriate discretization of the objective function. Numerical experiments confirm the convergence rates.
منابع مشابه
Approximation of Sparse Controls in Semilinear Elliptic Equations
Semilinear elliptic optimal control problems involving the L norm of the control in the objective are considered. Necessary and sufficient second-order optimality conditions are derived. A priori finite element error estimates for three different discretizations for the control problem are given. These discretizations differ in the use of piecewise constant, piecewise linear and continuous or n...
متن کاملHYBRID FUNCTIONS APPROACH AND PIECEWISE CONSTANT FUNCTION BY COLLOCATION METHOD FOR THE NONLINEAR VOLTERRA-FREDHOLM INTEGRAL EQUATIONS
In this work, we will compare two approximation method based on hybrid Legendre andBlock-Pulse functions and a computational method for solving nonlinear Fredholm-Volterraintegral equations of the second kind which is based on replacement of the unknown functionby truncated series of well known Block-Pulse functions (BPfs) expansion
متن کاملHybrid model predictive control of a nonlinear three-tank system based on the proposed compact form of piecewise affine model
In this paper, a predictive control based on the proposed hybrid model is designed to control the fluid height in a three-tank system with nonlinear dynamics whose operating mode depends on the instantaneous amount of system states. The use of nonlinear hybrid model in predictive control leads to a problem of mixed integer nonlinear programming (MINLP) which is very complex and time consuming t...
متن کاملSuperconvergence for Neumann boundary control problems governed by semilinear elliptic equations
This paper is concerned with the discretization error analysis of semilinear Neumann boundary control problems in polygonal domains with pointwise inequality constraints on the control. The approximations of the control are piecewise constant functions. The state and adjoint state are discretized by piecewise linear finite elements. In a postprocessing step approximations of locally optimal con...
متن کاملA Posteriori Error Estimates for Semilinear Boundary Control Problems
In this paper we study the finite element approximation for boundary control problems governed by semilinear elliptic equations. Optimal control problems are very important model in science and engineering numerical simulation. They have various physical backgrounds in many practical applications. Finite element approximation of optimal control problems plays a very important role in the numeri...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- Numerische Mathematik
دوره 122 شماره
صفحات -
تاریخ انتشار 2012