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This work presents, analyzes and tests stabilized space-time finite element methods on fully unstructured simplicial space-time meshes for the numerical solution of space-time tracking parabolic optimal control problems with the standard…

Numerical Analysis · Mathematics 2021-03-03 Ulrich Langer , Andreas Schafelner

We consider variational discretization of a parabolic optimal control problem governed by space-time measure controls. For the state discretization we use a Petrov-Galerkin method employing piecewise constant states and piecewise linear and…

Optimization and Control · Mathematics 2019-11-25 Evelyn Herberg , Michael Hinze , Henrik Schumacher

A continuous optimal control problem governed by an elliptic variational inequality was considered in Boukrouche-Tarzia, Comput. Optim. Appl., 53 (2012), 375-392 where the control variable is the internal energy $g$. It was proved the…

Numerical Analysis · Mathematics 2015-05-18 Mariela Olguín , Domingo A. Tarzia

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

We provide a framework for the numerical approximation of distributed optimal control problems, based on least-squares finite element methods. Our proposed method simultaneously solves the state and adjoint equations and is $\inf$--$\sup$…

Numerical Analysis · Mathematics 2023-08-03 Thomas Führer , Michael Karkulik

We present a fully discrete finite element method for the interior null controllability problem subject to the wave equation. For the numerical scheme, piece-wise affine continuous elements in space and finite differences in time are…

Numerical Analysis · Mathematics 2023-05-10 Erik Burman , Ali Feizmohammadi , Lauri Oksanen

We propose, analyze, and test new robust iterative solvers for systems of linear algebraic equations arising from the space-time finite element discretization of reduced optimality systems defining the approximate solution of hyperbolic…

Numerical Analysis · Mathematics 2024-04-08 Ulrich Langer , Richard Löscher , Olaf Steinbach , Huidong Yang

This paper aims to study the convergence of adaptive finite element method for control constrained elliptic optimal control problems under $L^2$-norm. We prove the contraction property and quasi-optimal complexity for the $L^2$-norm errors…

Numerical Analysis · Mathematics 2016-11-16 Wei Gong , Ningning Yan , Zhaojie Zhou

As opposed to the distributed control of parabolic PDE's, very few contributions currently exist pertaining to the Dirichlet boundary condition control for parabolic PDE's. This motivates our interest in the Dirichlet boundary condition…

Optimization and Control · Mathematics 2023-08-08 Aleš Wodecki , Pavel Strachota , Tomáš Oberhuber , Kateřina Škardová , Monika Balázsová

Finite element methods for a model elliptic distributed optimal control problem with pointwise state constraints are considered from the perspective of fourth order boundary value problems.

Numerical Analysis · Mathematics 2020-08-20 Susanne C. Brenner

We consider the design of structure-preserving discretization methods for the solution of systems of boundary controlled Partial Differential Equations (PDEs) thanks to the port-Hamiltonian formalism. We first provide a novel general…

Numerical Analysis · Mathematics 2020-09-30 Andrea Brugnoli , Ghislain Haine , Anass Serhani , Xavier Vasseur

We consider an optimal control problem governed by a one-dimensional elliptic equation that involves univariate functions of bounded variation as controls. For the discretization of the state equation we use linear finite elements and for…

Optimization and Control · Mathematics 2019-06-18 Dominik Hafemeyer , Florian Mannel , Ira Neitzel , Boris Vexler

In this work, first we employ a penalization technique to analyze a Dirichlet boundary feedback control problem pertaining to reaction-diffusion equation. We establish the stabilization result of the equivalent Robin problem in the…

Numerical Analysis · Mathematics 2026-03-25 Sudeep Kundu , Shishu pal Singh

This work presents and analyzes space-time finite element methods on fully unstructured simplicial space-time meshes for the numerical solution of parabolic optimal control problems. Using Babu\v{s}ka's theorem, we show well-posedness of…

Numerical Analysis · Mathematics 2020-04-07 Ulrich Langer , Olaf Steinbach , Fredi Tröltzsch , Huidong Yang

In this paper we investigate a priori error estimates for the space-time Galerkin finite element discretization of a simplified semilinear gradient enhanced damage model. The model equations are of a special structure as the state equation…

Optimization and Control · Mathematics 2020-04-14 Marita Holtmannspötter , Arnd Rösch

We consider an unconstrained tangential Dirichlet boundary control problem for the Stokes equations with an $ L^2 $ penalty on the boundary control. The contribution of this paper is twofold. First, we obtain well-posedness and regularity…

Numerical Analysis · Mathematics 2025-07-10 Wei Gong , Weiwei Hu , Mariano Mateos , John R. Singler , Yangwen Zhang

The paper deals with a stochastic Galerkin approximation of elliptic Dirichlet boundary control problems with random input data. The expectation of a tracking cost functional with the deterministic constrained control is minimized. Error…

Optimization and Control · Mathematics 2025-06-16 Max Winkler , Hamdullah Yücel

This paper is concerned with the development of weak Galerkin (WG) finite element method for optimal control problems governed by second order elliptic partial differential equations (PDEs). It is advantageous to use discontinuous finite…

Numerical Analysis · Mathematics 2023-10-03 Chunmei Wang , Junping Wang , Shangyou Zhang

A discretization of an optimal control problem of a stochastic parabolic equation driven by multiplicative noise is analyzed. The state equation is discretized by the continuous piecewise linear element method in space and by the backward…

Numerical Analysis · Mathematics 2021-02-23 Binjie Li

In this paper we investigate a priori error estimates for the space-time Galerkin finite element discretization of an optimal control problem governed by a simplified linear gradient enhanced damage model. The model equations are of a…

Numerical Analysis · Mathematics 2020-04-10 Marita Holtmannspötter , Arnd Rösch , Boris Vexler