A non-overlapping DDM combined with the characteristic method for optimal control problems governed by convection-diffusion equations

DOI10.1007/s10589-018-0008-0zbMath1410.90242OpenAlexW2804812437WikidataQ129798536 ScholiaQ129798536MaRDI QIDQ1790685

Keying Ma, Tong-jun Sun

Publication date: 2 October 2018

Published in: Computational Optimization and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10589-018-0008-0

zbMATH Keywords

error estimatesconvection-diffusion equationsoptimal control problemsintegral mean methodnon-overlapping DDM

Mathematics Subject Classification ID

Multigrid methods; domain decomposition for boundary value problems involving PDEs (65N55) Numerical methods based on necessary conditions (49M05) Approximation methods and heuristics in mathematical programming (90C59) Programming in abstract spaces (90C48) Numerical aspects of the method of characteristics for initial value and initial-boundary value problems involving PDEs (65M25) Existence theories for optimal control problems involving partial differential equations (49J20)

Related Items

The characteristic difference DDM for solving the time-fractional order convection-diffusion equations ⋮ The mass‐conserving domain decomposition method for convection diffusion equations with variable coefficients ⋮ An efficient characteristic finite difference s-DDM scheme for convection-diffusion equations ⋮ \textit{A posteriori} error estimates of characteristic mixed finite elements for convection-diffusion control problems

Cites Work

• Domain decomposition procedures combined with \(H^1\)-Galerkin mixed finite element method for parabolic equation
• Parallel Galerkin domain decomposition procedures based on the streamline diffusion method for convection-diffusion problems
• A priori error estimates for optimal control problems governed by transient advection-diffusion equations
• Adaptive finite element approximation for a constrained optimal control problem via multi-meshes
• Convergence analysis of an approximation of miscible displacement in porous media by mixed finite elements and a modified method of characteristics
• A spatial domain decomposition method for parabolic optimal control problems
• A priori and a posteriori error analysis of edge stabilization Galerkin method for the optimal control problem governed by convection-dominated diffusion equation
• Convergence and nonlinear stability of the Lagrange-Galerkin method for the Navier-Stokes equations
• Domain decomposition, optimal control of systems governed by partial differential equations, and synthesis of feedback laws
• Domain decomposition methods in optimal control of partial differential equations
• Optimal control of the convection-diffusion equation using stabilized finite element methods
• Domain decomposition methods for advection-dominated linear-quadratic elliptic optimal control problems
• Numerical treatment of partial differential equations. Revised translation of the 3rd German edition of `Numerische Behandlung partieller Differentialgleichungen' by Martin Stynes.
• Parallel Galerkin domain decomposition procedures for wave equation
• Local Error Estimates for SUPG Solutions of Advection-Dominated Elliptic Linear-Quadratic Optimal Control Problems
• Dynamic parallel Galerkin domain decomposition procedures with grid modification for parabolic equation
• Maximum Norm Estimates in the Finite Element Method on Plane Polygonal Domains. Part 2, Refinements
• Parallel Galerkin domain decomposition procedures for parabolic equation on general domain
• Galerkin domain decomposition procedures for parabolic equations on rectangular domain
• Neumann--Neumann Domain Decomposition Preconditioners for Linear-Quadratic Elliptic Optimal Control Problems
• Time Stepping Along Characteristics with Incomplete Iteration for a Galerkin Approximation of Miscible Displacement in Porous Media
• Numerical Methods for Convection-Dominated Diffusion Problems Based on Combining the Method of Characteristics with Finite Element or Finite Difference Procedures
• Explicit/Implicit Conservative Galerkin Domain Decomposition Procedures for Parabolic Problems
• Maximum Norm Estimates in the Finite Element Method on Plane Polygonal Domains. Part 1
• Adaptive Lagrange–Galerkin methods for unsteady convection-diffusion problems
• A Domain Decomposition Method with Coupled Transmission Conditions for the Optimal Control of Systems Governed by Elliptic Partial Differential Equations
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