相关论文: Finite element error analysis of affine optimal co…
We consider an inverse problem involving the reconstruction of the solution to a nonlinear partial differential equation (PDE) with unknown boundary conditions. Instead of direct boundary data, we are provided with a large dataset of…
We construct and analyze a multiscale finite element method for an elliptic distributed optimal control problem with pointwise control constraints, where the state equation has rough coefficients. We show that the performance of the…
In this article we study optimal control problems for systems that are affine with respect to some of the control variables and nonlinear in relation to the others. We consider finitely many equality and inequality constraints on the…
This work is concerned with quasi-optimal a-priori finite element error estimates for the obstacle problem in the $L^2$-norm. The discrete approximations are introduced as solutions to a finite element discretization of an accordingly…
We propose in this paper a multilevel correction method to solve optimal control problems constrained by elliptic equations with the finite element method. In this scheme, solving optimization problem on the finest finite element space is…
The numerical analysis of a family of distributed mixed optimal control problems governed by elliptic variational inequalities (with parameter $\alpha >0$) is obtained through the finite element method when its parameter $h\rightarrow 0$.…
In this paper, we investigate optimal control problems subject to a semilinear elliptic partial differential equations. The cost functional contains a term that measures the size of the support of the control, which is the so-called…
We investigate optimal control problems governed by the elliptic partial differential equation $-\Delta u=f$ subject to Dirichlet boundary conditions on a given domain $\Omega$. The control variable in this setting is the right-hand side…
The purpose of this work is the design and analysis of a reliable and efficient a posteriori error estimator for the so-called pointwise tracking optimal control problem. This linear-quadratic optimal control problem entails the…
We consider some boundary value tracking optimal control problem constrained by a Neumann boundary value problem for some elliptic partial differential equation where the control acts as right-hand side. This optimal control problem can be…
We study the numerical approximation of linear-quadratic optimal control problems subject to the fractional Laplace equation with its spectral definition. We compute an approximation of the state equation using a discretization of the…
In this paper we study partial-approximate controllability of semilinear nonlocal fractional evolution equations in Hilbert spaces. By using fractional calculus, variational approach and approximating technique, we give the approximate…
A multilevel adaptive refinement strategy for solving linear elliptic partial differential equations with random data is recalled in this work. The strategy extends the a posteriori error estimation framework introduced by Guignard and…
This article is concerned with the nonconforming finite element method for distributed elliptic optimal control problems with pointwise constraints on the control and gradient of the state variable. We reduce the minimization problem into a…
Inspired by applications in optimal control of semilinear elliptic partial differential equations and physics-integrated imaging, differential equation constrained optimization problems with constituents that are only accessible through…
We analyze the finite element discretization of distributed elliptic optimal control problems with variable energy regularization, where the usual $L^2(\Omega)$ norm regularization term with a constant regularization parameter $\varrho$ is…
This paper continues the investigations from [7] and is concerned with the derivation of first-order conditions for a control constrained optimization problem governed by a non-smooth elliptic PDE. The control enters the state equation not…
In this paper, we investigate optimal control problems governed by the parabolic interface equation, in which the control acts on the interface. The solution to this problem exhibits low global regularity due to the jump of the coefficient…
A counterexample to uniqueness of global minimizers of semilinear optimal control problems is given. The lack of uniqueness occurs for a special choice of the state-target in the cost functional. Our arguments show also that, for some…
In this paper we propose a new finite element method for solving elliptic optimal control problems with pointwise state constraints, including the distributed controls and the Dirichlet or Neumann boundary controls. The main idea is to use…