A Goal-Oriented Reduced Basis Methods-Accelerated Generalized Polynomial Chaos Algorithm
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Publication:3179335
DOI10.1137/16M1055736zbMath1352.65012arXiv1601.00137MaRDI QIDQ3179335
Jiahua Jiang, Yanlai Chen, Akil C. Narayan
Publication date: 21 December 2016
Published in: SIAM/ASA Journal on Uncertainty Quantification (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1601.00137
Probabilistic models, generic numerical methods in probability and statistics (65C20) Error bounds for boundary value problems involving PDEs (65N15) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30)
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Cites Work
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- Reduced basis techniques for stochastic problems
- Parametric analytical preconditioning and its applications to the reduced collocation methods
- A natural-norm successive constraint method for inf-sup lower bounds
- A reduced basis approach for variational problems with stochastic parameters: application to heat conduction with variable Robin coefficient
- A certified natural-norm successive constraint method for parametric inf-sup lower bounds
- Reduced basis approximation and a posteriori error estimation for affinely parametrized elliptic coercive partial differential equations. Application to transport and continuum mechanics.
- A priori convergence theory for reduced-basis approximations of single-parameter elliptic partial differential equations
- An `empirical interpolation' method: Application to efficient reduced-basis discretization of partial differential equations
- Reduced collocation methods: Reduced basis methods in the collocation framework
- A new algorithm for high-dimensional uncertainty quantification based on dimension-adaptive sparse grid approximation and reduced basis methods
- A successive constraint linear optimization method for lower bounds of parametric coercivity and inf-sup stability constants
- A Survey of Projection-Based Model Reduction Methods for Parametric Dynamical Systems
- A prioriconvergence of the Greedy algorithm for the parametrized reduced basis method
- Convergence Rates for Greedy Algorithms in Reduced Basis Methods
- Efficient reduced-basis treatment of nonaffine and nonlinear partial differential equations
- A ‘best points’ interpolation method for efficient approximation of parametrized functions
- Generalized Jacobi Weights, Christoffel Functions, and Jacobi Polynomials
- The Wiener--Askey Polynomial Chaos for Stochastic Differential Equations
- On the Reduced Basis Method
- A posteriorierror bounds for reduced-basis approximations of parametrized parabolic partial differential equations
- A Weighted Reduced Basis Method for Elliptic Partial Differential Equations with Random Input Data
- Reduced Basis Methods for Parameterized Partial Differential Equations with Stochastic Influences Using the Karhunen--Loève Expansion
- Reduced Basis Collocation Methods for Partial Differential Equations with Random Coefficients
- Adaptive Smolyak Pseudospectral Approximations
- High-Order Collocation Methods for Differential Equations with Random Inputs