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We consider a pointwise tracking optimal control problem for a semilinear elliptic partial differential equation. We derive the existence of optimal solutions and analyze first and, necessary and sufficient, second order optimality…

Numerical Analysis · Mathematics 2021-12-16 Alejandro Allendes , Francisco Fuica , Enrique Otarola

We obtained estimates for first eigenvalues of the Dirichlet boundary value problem for elliptic operators in divergence form (i.e. for the principal frequency of non-homogeneous membranes) in bounded domains $\Omega \subset \mathbb C$…

Analysis of PDEs · Mathematics 2023-01-18 Vladimir Gol'dshtein , Valery Pchelintsev

In this paper, we generalize the chance optimization problems and introduce constrained volume optimization where enables us to obtain convex formulation for challenging problems in systems and control. We show that many different problems…

Optimization and Control · Mathematics 2017-02-01 Ashkan Jasour , Constantino Lagoa

The aim of this paper is to extend the global error estimation and control addressed in Lang and Verwer [SIAM J. Sci. Comput. 29, 2007] for initial value problems to finite difference solutions of semilinear parabolic partial differential…

Numerical Analysis · Mathematics 2018-02-16 Kristian Debrabant , Jens Lang

This paper analyzes an interface-unfitted numerical method for distributed optimal control problems governed by elliptic interface equations. We follow the variational discretization concept to discretize the optimal control problems, and…

Numerical Analysis · Mathematics 2018-10-05 Tao Wang , Chaochao Yang , Xiaoping Xie

In this paper, we consider elliptic boundary value problems with discontinuous coefficients and obtain the asymptotic optimal error estimate $\|u-u_k\|_{1,\Omega}\leqslant Ch|\ln h|^{1/2}\|u\|_{2,\Omega_1+\Omega_2}$ for triangle linear…

Numerical Analysis · Mathematics 2013-11-19 Jinchao Xu

In this article a special class of nonlinear optimal control problems involving a bilinear term in the boundary condition is studied. These kind of problems arise for instance in the identification of an unknown space-dependent Robin…

Numerical Analysis · Mathematics 2024-12-20 Max Winkler

This paper is concerned with the numerical approximation of the Dirichlet initial-boundary-value problem of nonlinear pseudo-parabolic equations with spectral methods. Error estimates for the semidiscrete Galerkin and collocation schemes…

Numerical Analysis · Mathematics 2020-02-26 Eduardo Abreu , Angel Durán

We investigate constrained optimal control problems for linear stochastic dynamical systems evolving in discrete time. We consider minimization of an expected value cost over a finite horizon. Hard constraints are introduced first, and then…

Optimization and Control · Mathematics 2011-07-07 Eugenio Cinquemani , Mayank Agarwal , Debasish Chatterjee , John Lygeros

We study two types of asymptotic problems whose common feature - and difficulty- is to exhibit oscillating Dirichlet boundary conditions : the main contribution of this article is to show how to recover the Dirichlet boundary condition for…

Analysis of PDEs · Mathematics 2012-05-22 Guy Barles , Elisabeth Mironescu

The aim of this work is to derive a priori error estimates for finite element discretizations of control--constrained optimal control problems that involve the Stokes system and Dirac measures. The first problem entails the minimization of…

Numerical Analysis · Mathematics 2020-04-29 Francisco Fuica , Enrique Otarola , Daniel Quero

In this paper we investigate the homogenization problem with a non-homogeneous Dirichlet condition. Our aim is to give error estimates with boundary data in $H^{1/2}(\partial\Omega)$. The tools used are those of the unfolding method in…

Numerical Analysis · Mathematics 2013-08-20 Georges Griso

This paper is concerned with the convergence of the solution of general elliptic boundary value problems in cylindrical domain, when some directions of the domain go to infinity.

Analysis of PDEs · Mathematics 2007-05-23 Bernard Brighi- Senoussi Guesmia

We study solution techniques for a linear-quadratic optimal control problem involving fractional powers of elliptic operators. These fractional operators can be realized as the Dirichlet-to-Neumann map for a nonuniformly elliptic problem…

Optimization and Control · Mathematics 2015-04-21 Harbir Antil , Enrique Otarola

We consider an elliptic optimal control problem where the objective functional contains evaluations of the state at a finite number of points. In particular, we use a fidelity term that encourages the state to take certain values at these…

Numerical Analysis · Mathematics 2014-11-19 C. Brett , A. S. Dedner , C. M. Elliott

We propose a new fictitious domain finite element method, well suited for elliptic problems posed in a domain given by a level-set function without requiring a mesh fitting the boundary. To impose the Dirichlet boundary conditions, we…

Numerical Analysis · Mathematics 2019-07-09 Michel Duprez , Alexei Lozinski

In this article we develop convergence theory for a class of goal-oriented adaptive finite element algorithms for second order nonsymmetric linear elliptic equations. In particular, we establish contraction results for a method of this type…

Numerical Analysis · Mathematics 2013-08-09 Michael Holst , Sara Pollock

We introduce a family of hybrid discretisations for the numerical approximation of optimal control problems governed by the equations of immiscible displacement in porous media. The proposed schemes are based on mixed and discontinuous…

Numerical Analysis · Mathematics 2019-05-02 S. Kumar , R. Ruiz Baier , R. Sandilya

This paper is concerned with boundary regularity estimates in the homogenization of elliptic equations with rapidly oscillating and high-contrast coefficients. We establish uniform nontangential-maximal-function estimates for the Dirichlet,…

Analysis of PDEs · Mathematics 2021-05-28 Zhongwei Shen

In this paper, we consider a family of simultaneous distributed-boundary optimal control problems ($P_{\alpha}$) on the internal energy and the heat flux for a system governed by a mixed elliptic variational equality with a parameter…

Optimization and Control · Mathematics 2023-03-30 Carolina M. Bollo , Claudia M. Gariboldi , Domingo A. Tarzia