A reduced-order two-grid method based on POD technique for the semilinear parabolic equation
DOI10.1016/j.apnum.2024.07.012zbMATH Open1546.65069MaRDI QIDQ6593437
Publication date: 26 August 2024
Published in: Applied Numerical Mathematics (Search for Journal in Brave)
proper orthogonal decompositionsemilinear parabolic equationerror estimatedegrees of freedomreduced-order two-grid
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) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) 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) Error bounds for initial value and initial-boundary value problems involving PDEs (65M15) Multigrid methods; domain decomposition for initial value and initial-boundary value problems involving PDEs (65M55) Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems (65M99) Semilinear parabolic equations (35K58)
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- \(L^p\) error estimates of two-grid method for miscible displacement problem
- A stabilized MFE reduced-order extrapolation model based on POD for the 2D unsteady conduction-convection problem
- Galerkin finite element methods for parabolic problems
- Two-grid finite volume element methods for semilinear parabolic problems
- Proper orthogonal decomposition approach and error estimation of mixed finite element methods for the tropical Pacific Ocean reduced gravity model
- Stochastic model reduction for chaos representations
- Unconditional optimal error estimates of a two-grid method for semilinear parabolic equation
- Proper orthogonal decomposition methods for partial differential equations
- Numerical analysis of a second-order IPDGFE method for the Allen-Cahn equation and the curvature-driven geometric flow
- Numerical analysis of an unconditionally energy-stable reduced-order finite element method for the Allen-Cahn phase field model
- The reduced-order method of continuous space-time finite element scheme for the non-stationary incompressible flows
- A reduced-order fast reproducing kernel collocation method for nonlocal models with inhomogeneous volume constraints
- A two-level stabilized nonconforming finite element method for the stationary Navier-Stokes equations
- A non-intrusive reduced basis approach for parametrized heat transfer problems
- Numerical solution of a miscible displacement problem with dispersion term using a two-grid mixed finite element approach
- A reduced-order extrapolation algorithm based on CNLSMFE formulation and POD technique for two-dimensional Sobolev equations
- Linearized reduced-order models for subsurface flow simulation
- An efficient two-grid method for the Cahn-Hilliard equation with the concentration-dependent mobility and the logarithmic Flory-Huggins bulk potential
- A reduced-order characteristic finite element method based on POD for optimal control problem governed by convection-diffusion equation
- An Online Manifold Learning Approach for Model Reduction of Dynamical Systems
- Two-Grid Methods for Maxwell Eigenvalue Problems
- A Two-Grid Finite Element Method for Time-Dependent Incompressible Navier-Stokes Equations with Non-Smooth Initial Data
- Closed-loop control of an open cavity flow using reduced-order models
- Input–output analysis, model reduction and control of the flat-plate boundary layer
- Turbulence and the dynamics of coherent structures. I. Coherent structures
- The discontinuous Galerkin method for semilinear parabolic problems
- A Novel Two-Grid Method for Semilinear Elliptic Equations
- A two-grid discretization scheme for eigenvalue problems
- A reduced-order approach for optimal control of fluids using proper orthogonal decomposition
- Model Reduction and Approximation
- Hierarchical Approximate Proper Orthogonal Decomposition
- Two-Grid Discretization Techniques for Linear and Nonlinear PDE<scp>s</scp>
- Error Estimates on a New Nonlinear Galerkin Method Based on Two-Grid Finite Elements
- System- and Data-Driven Methods and Algorithms
- Modified Two-Grid Algorithm for Nonlinear Power-Law Conductivity in Maxwell's Problems with High Accuracy
- An Efficient Two-Grid Scheme for the Cahn-Hilliard Equation
- Two‐grid methods for time‐harmonic Maxwell equations
- Reduced basis method for finite volume approximations of parametrized linear evolution equations
- A precision preserving Crank-Nicolson mixed finite element lowering dimension method for the unsteady conduction-convection problem
- Error estimate of the non-intrusive reduced basis (NIRB) two-grid method with parabolic equations
- POD-ROMs for Incompressible Flows Including Snapshots of the Temporal Derivative of the Full Order Solution
- Two-grid methods for Maxwell's equations in a Cole-Cole dispersive medium
This page was built for publication: A reduced-order two-grid method based on POD technique for the semilinear parabolic equation
