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In this paper, we present and analyze an interior penalty discontinuous Galerkin method for the distributed elliptic optimal control problems. It is based on a reconstructed discontinuous approximation which admits arbitrarily high-order…

Numerical Analysis · Mathematics 2026-01-05 Ruo Li , Haoyang Liu , Jun Yin

We present a posteriori error analysis in the supremum norm for the symmetric interior penalty discontinuous Galerkin method for the elliptic obstacle problem. We construct discrete barrier functions based on appropriate corrections of the…

Numerical Analysis · Mathematics 2021-08-27 Blanca Ayuso de Dios , Thirupathi Gudi , Kamana Porwal

In this article, an abstract framework for the error analysis of discontinuous Galerkin methods for control constrained optimal control problems is developed. The analysis establishes the best approximation result from a priori analysis…

Numerical Analysis · Mathematics 2014-11-05 Sudipto Chowdhury , Thirupathi Gudi , A. K. Nandakumaran

In this paper, we are concerned with a nonlinear optimal control problem of ordinary differential equations. We consider a discretization of the problem with the discontinuous Galerkin method with arbitrary order $r \in \mathbb{N}\cup…

Numerical Analysis · Mathematics 2020-05-25 Woocheol Choi , Young-Pil Choi

The analyses of interior penalty discontinuous Galerkin methods of any order k for solving elliptic and parabolic problems with Dirac line sources are presented. For the steady state case, we prove convergence of the method by deriving a…

Numerical Analysis · Mathematics 2022-07-19 Rami Masri , Boqian Shen , Beatrice Riviere

We investigate discontinuous Galerkin methods for an elliptic optimal control problem with a general state equation and pointwise state constraints on general polygonal domains. We show that discontinuous Galerkin methods for general…

Numerical Analysis · Mathematics 2023-09-04 Sijing Liu , Zhiyu Tan , Yi 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

In this paper, a space-time discontinuous Galerkin finite element method for distributed optimal control problems governed by unsteady diffusion-convection-reaction equations with control constraints is studied. Time discretization is…

Optimization and Control · Mathematics 2013-08-09 Tuğba Akman , Bülent Karasözen

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

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

An interior penalty discontinuous Galerkin method is devised to approximate minimizers of a linear folding model by discontinuous isoparametric finite element functions that account for an approximation of a folding arc. The numerical…

Numerical Analysis · Mathematics 2022-05-13 Sören Bartels , Andrea Bonito , Philipp Tscherner

In this paper we establish a best approximation property of fully discrete Galerkin finite element solutions of second order parabolic problems on convex polygonal and polyhedral domains in the $L^\infty$ norm. The discretization method…

Numerical Analysis · Mathematics 2018-08-20 Dmitriy Leykekhman , Boris Vexler

We propose a locally conservative enriched Galerkin scheme that preserves the physical bounds for an elliptic problem. To this end, we use a substantial over-penalization of the discrete solution's jumps to obtain optimal convergence. To…

Numerical Analysis · Mathematics 2025-12-19 Gabriel R. Barrenechea , Philip L. Lederer , Andreas Rupp

In this paper we establish best approximation property of fully discrete Galerkin solutions of second order parabolic problems on convex polygonal and polyhedral domains in the $L^\infty(I;W^{1,\infty}(\Om))$ norm. The discretization method…

Numerical Analysis · Mathematics 2018-08-20 Dmitriy Leykekhman , Boris Vexler

We propose an arbitrary-order discontinuous Galerkin method for second-order elliptic problem on general polygonal mesh with only one degree of freedom per element. This is achieved by locally solving a discrete least-squares over a…

Numerical Analysis · Mathematics 2019-11-26 Ruo Li , Pingbing Ming , Zhiyuan Sun , Zhijian Yang

This paper investigates a symmetric dual-wind discontinuous Galerkin (DWDG) method for solving an elliptic optimal control problem with control constraints. The governing constraint is an elliptic partial differential equation (PDE), which…

Numerical Analysis · Mathematics 2025-06-17 Satyajith Bommana Boyana , Thomas Lewis , Sijing Liu , Yi Zhang

We consider a semilinear parabolic equation with a large class of nonlinearities without any growth conditions. We discretize the problem with a discontinuous Galerkin scheme dG(0) in time (which is a variant of the implicit Euler scheme)…

Numerical Analysis · Mathematics 2018-08-17 Dominik Meidner , Boris Vexler

In this paper we propose and analyze a Discontinuous Galerkin method for a linear parabolic problem with dynamic boundary conditions. We present the formulation and prove stability and optimal a priori error estimates for the fully discrete…

Numerical Analysis · Mathematics 2015-01-21 Paola F. Antonietti , Maurizio Grasselli , Simone Stangalino , Marco Verani

In this paper, we propose a Galerkin finite element method for the elliptic optimal control problem governed by the Riesz space-fractional PDEs on 2D domains with control variable being discretized by variational discretization technique.…

Numerical Analysis · Mathematics 2022-02-22 Xiaogang Zhu

We propose a novel Galerkin discretization scheme for stochastic optimal control problems on an indefinite time horizon. The control problems are linear-quadratic in the controls, but possibly nonlinear in the state variables, and the…

Optimization and Control · Mathematics 2013-10-01 Ralf Banisch , Carsten Hartmann
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