Reduced basis techniques for stochastic problems (Q358488)

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English	Reduced basis techniques for stochastic problems	scientific article

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scholarly article

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Reduced basis techniques for stochastic problems (English)

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Ngoc Cuong Nguyen

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Sebastien Boyabal

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Anthony T. Patera

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Archives of Computational Methods in Engineering

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publication date

9 August 2013

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full work available at URL

https://arxiv.org/abs/1004.0357

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describes a project that uses

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MaRDI profile type

MaRDI publication profile

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Solving elliptic boundary value problems with uncertain coefficients by the finite element method: the stochastic formulation

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A Stochastic Collocation Method for Elliptic Partial Differential Equations with Random Input Data

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An `empirical interpolation' method: Application to efficient reduced-basis discretization of partial differential equations

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On the Reduced Basis Method

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An optimal control approach to <i>a posteriori</i> error estimation in finite element methods

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Variance reduction methods for CONNFFESSIT-like simulations

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Reduced-Basis Approach for Homogenization beyond the Periodic Setting

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A variance reduction method for parametrized stochastic differential equations using the reduced basis paradigm

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A reduced basis approach for variational problems with stochastic parameters: application to heat conduction with variable Robin coefficient

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POD and CVT-based reduced-order modeling of Navier-Stokes flows

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Solution of stochastic partial differential equations using Galerkin finite element techniques

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Numerical Challenges in the Use of Polynomial Chaos Representations for Stochastic Processes

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Reduced Basis Error Bound Computation of Parameter-Dependent Navier–Stokes Equations by the Natural Norm Approach

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On the Error Behavior of the Reduced Basis Technique for Nonlinear Finite Element Approximations

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<i>A posteriori</i>error bounds for reduced-basis approximations of parametrized parabolic partial differential equations

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Efficient reduced-basis treatment of nonaffine and nonlinear partial differential equations

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Reduced basis method for finite volume approximations of parametrized linear evolution equations

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Reduced basis approximation anda posteriori error estimation for stress intensity factors

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A successive constraint linear optimization method for lower bounds of parametric coercivity and inf-sup stability constants

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A natural-norm successive constraint method for inf-sup lower bounds

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A Certified Reduced Basis Method for the Fokker–Planck Equation of Dilute Polymeric Fluids: FENE Dumbbells in Extensional Flow

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Galerkin Proper Orthogonal Decomposition Methods for a General Equation in Fluid Dynamics

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Multiscale Modelling of Complex Fluids: A Mathematical Initiation

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Estimation of the Error in the Reduced Basis Method Solution of Differential Algebraic Equation Systems

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Functional quantization of Gaussian processes

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A priori convergence theory for reduced-basis approximations of single-parameter elliptic partial differential equations

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A general multipurpose interpolation procedure: The magic points

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Galerkin methods for linear and nonlinear elliptic stochastic partial differential equations

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Modal representation of geometrically nonlinear behavior by the finite element method

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Variance Reduction for Simulated Diffusions

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A multiscale reduced-basis method for parametrized elliptic partial differential equations with multiple scales

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Reduced basis approximation and a posteriori error estimation for the time-dependent viscous Burgers' equation

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Recent advances in reduction methods for nonlinear problems

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Multiple-parameter reduced basis technique for bifurcation and post-buckling analyses of composite plates

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Recent advances in reduction methods for instability analysis of structures

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Reduction methods for nonlinear steady-state thermal analysis

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A generalized spectral decomposition technique to solve a class of linear stochastic partial differential equations

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Generalized spectral decomposition method for solving stochastic finite element equations: invariant subspace problem and dedicated algorithms

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Functional quantization for numerics with an application to option pricing

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Convergence of Multi-Dimensional Quantized SDE’s

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Reduced basis approximation and a posteriori error estimation for a Boltzmann model

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The Reduced Basis Method for Incompressible Viscous Flow Calculations

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Estimation of the Error in the Reduced Basis Method Solution of Nonlinear Equations

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The Reduced Basis Method for Initial Value Problems

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Numerical models for differential problems. Translated by Silvia Quarteroni.

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Numerical analysis of continuation methods for nonlinear structural problems

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On the theory and error estimation of the reduced basis method for multi-parameter problems

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Reduced basis approximation and a posteriori error estimation for affinely parametrized elliptic coercive partial differential equations. Application to transport and continuum mechanics.

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Karhunen-Loève approximation of random fields by generalized fast multipole methods

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``Natural norm'' a posteriori error estimators for reduced basis approximations

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Nonlinear methods of approximation

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<b><i>A Posteriori</i></b>Error Estimation for Reduced-Basis Approximation of Parametrized Elliptic Coercive Partial Differential Equations: “Convex Inverse” Bound Conditioners

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Identifiers

zbMATH Open document ID

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10.1007/s11831-010-9056-z

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Mathematics Subject Classification ID

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zbMATH DE Number

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Sitelinks

Mathematics(1 entry)

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