A discontinuous Galerkin method for optimal control problems governed by a system of convection-diffusion PDEs with nonlinear reaction terms
DOI10.1016/j.camwa.2015.09.006zbMath1443.65380OpenAlexW1963444436WikidataQ115223981 ScholiaQ115223981MaRDI QIDQ2006523
Martin Stoll, Hamdullah Yücel, Peter Benner
Publication date: 11 October 2020
Published in: Computers \& Mathematics with Applications (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/j.camwa.2015.09.006
preconditioningdiscontinuous Galerkin methodoptimal control problema posteriori error estimateconvection dominated equation
Optimality conditions for problems involving partial differential equations (49K20) Error bounds for boundary value problems involving PDEs (65N15) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Existence theories for optimal control problems involving partial differential equations (49J20) Discrete approximations in optimal control (49M25) PDEs in connection with control and optimization (35Q93)
Related Items (13)
Cites Work
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- Analysis of stabilized higher-order finite element approximation of nonstationary and nonlinear convection-diffusion-reaction equations
- Adaptive discontinuous Galerkin methods for state constrained optimal control problems governed by convection diffusion equations
- Finite element methods for time-dependent convection-diffusion-reaction equations with small diffusion
- A priori and a posteriori error analysis of edge stabilization Galerkin method for the optimal control problem governed by convection-dominated diffusion equation
- Chebyshev semi-iteration in preconditioning for problems including the mass matrix
- A robust a-posteriori error estimator for discontinuous Galerkin methods for convection-diffusion equations
- A one-dimensional reaction/diffusion system with a fast reaction
- A posteriori error estimates for control problems governed by nonlinear elliptic equations
- Runge--Kutta discontinuous Galerkin methods for convection-dominated problems
- Investigation of commutative properties of discontinuous Galerkin methods in PDE constrained optimal control problems
- ERROR ESTIMATES IN THE APPROXIMATION OF OPTIMIZATION PROBLEMS GOVERNED BY NONLINEAR OPERATORS
- Distributed Optimal Control of Diffusion-Convection-Reaction Equations Using Discontinuous Galerkin Methods
- Local discontinuous galerkin approximation of convection‐dominated diffusion optimal control problems with control constraints
- Optimal boundary control of a system of reaction diffusion equations
- Local Error Estimates for SUPG Solutions of Advection-Dominated Elliptic Linear-Quadratic Optimal Control Problems
- Local Error Analysis of Discontinuous Galerkin Methods for Advection-Dominated Elliptic Linear-Quadratic Optimal Control Problems
- Numerical solution of saddle point problems
- ENERGY NORM A POSTERIORI ERROR ESTIMATION OF hp-ADAPTIVE DISCONTINUOUS GALERKIN METHODS FOR ELLIPTIC PROBLEMS
- Discontinuous Galerkin Methods for Solving Elliptic and Parabolic Equations
- GMRES: A Generalized Minimal Residual Algorithm for Solving Nonsymmetric Linear Systems
- A Posteriori Error Estimates for a Discontinuous Galerkin Approximation of Second-Order Elliptic Problems
- A Note on Preconditioning for Indefinite Linear Systems
- On optimization techniques for solving nonlinear inverse problems
- Unified Analysis of Discontinuous Galerkin Methods for Elliptic Problems
- Discontinuoushp-Finite Element Methods for Advection-Diffusion-Reaction Problems
- A Convergent Adaptive Algorithm for Poisson’s Equation
- Adaptive Finite Element Methods for PDE-Constrained Optimal Control Problems
- A Primal-Dual Active Set Strategy for Optimal Boundary Control of a Nonlinear Reaction-Diffusion System
- Adaptive Symmetric Interior Penalty Galerkin (SIPG) method for optimal control of convection diffusion equations with control constraints
- Robust A Posteriori Error Estimates for Stationary Convection-Diffusion Equations
- Optimal control and numerical adaptivity for advection–diffusion equations
- A Method for the Numerical Calculation of Hydrodynamic Shocks
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