POD reduced-order modeling for evolution equations utilizing arbitrary finite element discretizations
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Publication:1756929
DOI10.1007/s10444-018-9620-xzbMath1404.65264arXiv1701.05054OpenAlexW2582992792WikidataQ129618491 ScholiaQ129618491MaRDI QIDQ1756929
Publication date: 28 December 2018
Published in: Advances in Computational Mathematics (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1701.05054
proper orthogonal decompositionevolution equationspartial differential equationmodel order reductionadaptive finite element discretization
Numerical mathematical programming methods (65K05) Nonlinear parabolic equations (35K55) Abstract parabolic equations (35K90) Heat equation (35K05) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30)
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Cites Work
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- Automated solution of differential equations by the finite element method. The FEniCS book
- Error estimates for abstract linear-quadratic optimal control problems using proper orthogonal decomposition
- Semigroups of linear operators and applications to partial differential equations
- Hamiltonian Pontryagin's principles for control problems governed by semilinear parabolic equations
- POD-Galerkin reduced-order modeling with adaptive finite element snapshots
- Design of adaptive finite element software. The finite element toolbox ALBERTA. With CD-ROM
- An `empirical interpolation' method: Application to efficient reduced-basis discretization of partial differential equations
- Control of the Burgers equation by a reduced-order approach using proper orthogonal decomposition
- Reduced basis methods with adaptive snapshot computations
- Optimal Control of a Phase-Field Model Using Proper Orthogonal Decomposition
- A New Selection Operator for the Discrete Empirical Interpolation Method---Improved A Priori Error Bound and Extensions
- A minimum-residual mixed reduced basis method: Exact residual certification and simultaneous finite-element reduced-basis refinement
- THERMODYNAMICALLY CONSISTENT, FRAME INDIFFERENT DIFFUSE INTERFACE MODELS FOR INCOMPRESSIBLE TWO-PHASE FLOWS WITH DIFFERENT DENSITIES
- Nonlinear Model Reduction via Discrete Empirical Interpolation
- An adaptive finite-element Moreau–Yosida-based solver for a non-smooth Cahn–Hilliard problem
- Nonlinear model reduction based on the finite element method with interpolated coefficients: Semilinear parabolic equations
- Optimization with PDE Constraints
- Reduced‐order modelling of an adaptive mesh ocean model
- A ‘best points’ interpolation method for efficient approximation of parametrized functions
- Abstract Parabolic Evolution Equations and their Applications
- Turbulence and the dynamics of coherent structures. I. Coherent structures
- The Cahn–Hilliard gradient theory for phase separation with non-smooth free energy Part I: Mathematical analysis
- Galerkin Proper Orthogonal Decomposition Methods for a General Equation in Fluid Dynamics
- Efficient Implementation of Finite Element Methods on Nonmatching and Overlapping Meshes in Three Dimensions
- Missing Point Estimation in Models Described by Proper Orthogonal Decomposition
- Model Order Reduction in Fluid Dynamics: Challenges and Perspectives
- Free Energy of a Nonuniform System. I. Interfacial Free Energy
- Nonlinear Model Order Reduction via Dynamic Mode Decomposition
- Turbulence, Coherent Structures, Dynamical Systems and Symmetry
- New POD Error Expressions, Error Bounds, and Asymptotic Results for Reduced Order Models of Parabolic PDEs
- Three control methods for time-dependent fluid flow
- Galerkin proper orthogonal decomposition methods for parabolic problems