A posteriori error estimation for the stochastic collocation finite element approximation of the heat equation with random coefficients
DOI10.1007/978-3-030-81362-8_6zbMath1497.65192OpenAlexW4253762515MaRDI QIDQ2091294
Publication date: 1 November 2022
Full work available at URL: https://doi.org/10.1007/978-3-030-81362-8_6
Heat equation (35K05) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs (65M70) Error bounds for initial value and initial-boundary value problems involving PDEs (65M15) Computational methods for stochastic equations (aspects of stochastic analysis) (60H35) Probabilistic methods, particle methods, etc. for initial value and initial-boundary value problems involving PDEs (65M75) Numerical approximation of high-dimensional functions; sparse grids (65D40)
Related Items (1)
Uses Software
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- ALEA
- Convergence of quasi-optimal sparse-grid approximation of Hilbert-space-valued functions: Application to random elliptic PDEs
- High-dimensional adaptive sparse polynomial interpolation and applications to parametric PDEs
- Adaptive stochastic Galerkin FEM
- A unified approach to a posteriori error estimation using element residual methods
- Dimension-adaptive tensor-product quadrature
- Adaptive finite elements for a linear parabolic problem
- High dimensional polynomial interpolation on sparse grids
- A posteriori error estimation and adaptivity in stochastic Galerkin FEM for parametric elliptic PDEs: beyond the affine case
- A posteriori error estimates for finite element discretizations of the heat equation
- Adaptive finite element methods for diffusion and convection problems
- An Adaptive Sparse Grid Algorithm for Elliptic PDEs with Lognormal Diffusion Coefficient
- Energy Norm A Posteriori Error Estimation for Parametric Operator Equations
- Stochastic Spectral Galerkin and Collocation Methods for PDEs with Random Coefficients: A Numerical Comparison
- ON THE OPTIMAL POLYNOMIAL APPROXIMATION OF STOCHASTIC PDES BY GALERKIN AND COLLOCATION METHODS
- Adaptive Finite Element Methods for Parabolic Problems I: A Linear Model Problem
- A posteriori error estimates for the Crank–Nicolson method for parabolic equations
- A convergent adaptive stochastic Galerkin finite element method with quasi-optimal spatial meshes
- An Anisotropic Error Estimator for the Crank–Nicolson Method: Application to a Parabolic Problem
- Spectral Methods for Uncertainty Quantification
- A Sparse Grid Stochastic Collocation Method for Partial Differential Equations with Random Input Data
- An Anisotropic Sparse Grid Stochastic Collocation Method for Partial Differential Equations with Random Input Data
- Analysis of the Efficiency of an a Posteriori Error Estimator for Linear Triangular Finite Elements
- A‐posteriori error estimates for the finite element method
- Error Estimates for Adaptive Finite Element Computations
- A Posteriori Error Estimates for Nonlinear Problems. Finite Element Discretizations of Elliptic Equations
- A Posteriori Error Estimation for the Stochastic Collocation Finite Element Method
- Error estimates for some quasi-interpolation operators
- Adaptive Finite Element Methods for Parabolic Problems II: Optimal Error Estimates in $L_\infty L_2 $ and $L_\infty L_\infty $
- Robust a posteriori error estimation for parameter-dependent linear elasticity equations
- Efficient Adaptive Multilevel Stochastic Galerkin Approximation Using Implicit A Posteriori Error Estimation
- High-Order Collocation Methods for Differential Equations with Random Inputs
- A Stochastic Collocation Method for Elliptic Partial Differential Equations with Random Input Data
This page was built for publication: A posteriori error estimation for the stochastic collocation finite element approximation of the heat equation with random coefficients
