Journal ArticleDOI
A Priori Error Estimates for Space-Time Finite Element Discretization of Parabolic Optimal Control Problems Part II: Problems with Control Constraints
MeidnerDominik,VexlerBoris +1 more
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In this article, the second part of a priori error analysis for finite element discretizations of parabolic optimal control problems is presented, where the authors consider the problem of discretization of finite element control problems.Abstract:
This paper is the second part of our work on a priori error analysis for finite element discretizations of parabolic optimal control problems. In the first part [SIAM J. Control Optim., 47 (2008), ...read more
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Journal ArticleDOI
Adaptive Space-Time Finite Element Methods for Parabolic Optimization Problems
Dominik Meidner,Boris Vexler +1 more
TL;DR: In this article, a posteriori error estimate for space-time finite element discretizations of parabolic optimization problems is derived for a given quantity of interest and separate the influences of different parts of the discretization.
Journal ArticleDOI
A priori error estimates for space–time finite element discretization of semilinear parabolic optimal control problems
Ira Neitzel,Boris Vexler +1 more
TL;DR: A priori error estimates for space–time finite element discretizations of optimal control problems governed by semilinear parabolic PDEs and subject to pointwise control constraints are derived.
Journal ArticleDOI
A priori error estimates for elliptic optimal control problems with a bilinear state equation
Axel Kröner,Boris Vexler +1 more
TL;DR: A priori error estimates for the discretization error in the control variable are derived and theoretical results by numerical examples are confirmed.
Journal ArticleDOI
Efficient numerical realization of discontinuous Galerkin methods for temporal discretization of parabolic problems
TL;DR: An efficient and easy to implement approach to solving the semidiscrete equation systems resulting from time discretization of nonlinear parabolic problems with discontinuous Galerkin methods of order r, based on applying Newton’s method and decoupling the Newton update equation.
Book ChapterDOI
A Priori Error Estimates for Space-Time Finite Element Discretization of Parabolic Optimal Control Problems
Dominik Meidner,Boris Vexler +1 more
TL;DR: This article summarizes recent results on a priori error estimates for space-time finite element discretizations of linear-quadratic parabolic optimal control problems and considers three cases: problems without inequality constraints, problems with pointwise control constraints, and problems with state constraints pointwise in time.