Local a posteriori error analysis of finite element method for parabolic boundary control problems
DOI10.1007/s10915-022-01788-wzbMath1484.65227OpenAlexW4214515842MaRDI QIDQ2113661
Rajen Kumar Sinha, Ram P. Manohar
Publication date: 14 March 2022
Published in: Journal of Scientific Computing (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/s10915-022-01788-w
finite element methodparabolic partial differential equationsbackward-Euler methodNeumann boundary control problemslocal a posteriori error estimates
Control/observation systems governed by partial differential equations (93C20) Initial-boundary value problems for second-order parabolic equations (35K20) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs (65N50) PDE constrained optimization (numerical aspects) (49M41)
Cites Work
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- Discrete maximal parabolic regularity for Galerkin finite element methods
- A posteriori error estimates for optimal distributed control governed by the evolution equations
- Finite element methods (Part 1)
- A posteriori error estimates for some model boundary control problems
- Augmented Lagrangian methods for nonsmooth, convex optimization in Hilbert spaces
- A posteriori error estimates for optimal control problems governed by parabolic equations
- Error estimates for parabolic optimal control problems with control constraints
- Finite element method and a priori error estimates for Dirichlet boundary control problems governed by parabolic PDEs
- A Posteriori Error Estimates for Convex Boundary Control Problems
- Recovery Type A Posteriori Error Estimates of Fully Discrete Finite Element Methods for General Convex Parabolic Optimal Control Problems
- Functional A Posteriori Error Estimates for Time-Periodic Parabolic Optimal Control Problems
- Dirichlet boundary control for a parabolic equation with a final observation I: A space–time mixed formulation and penalization
- Finite Element Interpolation of Nonsmooth Functions Satisfying Boundary Conditions
- Ana posteriorierror analysis of adaptive finite element methods for distributed elliptic control problems with control constraints
- Local A Posteriori Error Estimates for Convex Boundary Control Problems
- A Priori Error Estimates for Space-Time Finite Element Discretization of Parabolic Optimal Control Problems Part I: Problems Without Control Constraints
- A Priori Error Estimates for Space-Time Finite Element Discretization of Parabolic Optimal Control Problems Part II: Problems with Control Constraints
- Adaptive Finite Element Methods for Optimal Control of Partial Differential Equations: Basic Concept
- Adaptive Finite Element Approximation for Distributed Elliptic Optimal Control Problems
- Primal-Dual Active Set Strategy for a General Class of Constrained Optimal Control Problems
- Parabolic Control Problems in Measure Spaces with Sparse Solutions
- New development in freefem++
- Local and parallel finite element algorithms based on two-grid discretizations
- Goal-Oriented Adaptivity in Control Constrained Optimal Control of Partial Differential Equations
- A Priori Error Analysis for Finite Element Approximation of Parabolic Optimal Control Problems with Pointwise Control
- Mesh adaptation for stationary flow control
- A posteriori error estimates for distributed convex optimal control problems