Solving Log-Transformed Random Diffusion Problems by Stochastic Galerkin Mixed Finite Element Methods

DOI10.1137/14100097XzbMath1325.65018MaRDI QIDQ2945164

Catherine E. Powell, Elisabeth Ullmann

Publication date: 9 September 2015

Published in: SIAM/ASA Journal on Uncertainty Quantification (Search for Journal in Brave)

zbMATH Keywords

preconditioningsecond-order elliptic problemsmixed finite elementsconvection-diffusionnumerical experimentgeneralized saddle point problemsstochastic finite elementsSchur complement approximationKrylov subspace iterationPDEs with random datageneralized minimal residual (GMRES) iterationstochastic Galerkin finite element

Mathematics Subject Classification ID

Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Iterative numerical methods for linear systems (65F10) Stochastic partial differential equations (aspects of stochastic analysis) (60H15) PDEs with randomness, stochastic partial differential equations (35R60) Computational methods for stochastic equations (aspects of stochastic analysis) (60H35) Numerical solutions to stochastic differential and integral equations (65C30) Preconditioners for iterative methods (65F08)

Related Items (3)

Convergence analysis of multifidelity Monte Carlo estimation ⋮ A resilient domain decomposition polynomial chaos solver for uncertain elliptic PDEs ⋮ A computational study of preconditioning techniques for the stochastic diffusion equation with lognormal coefficient

Uses Software

• OPQ

Cites Work

• Finite Elements and Fast Iterative Solvers
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• A Priori Error Analysis of Stochastic Galerkin Mixed Approximations of Elliptic PDEs with Random Data
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• $H( {div})$ preconditioning for a mixed finite element formulation of the diffusion problem with random data
• Existence, Uniqueness and Approximation for Generalized Saddle Point Problems
• Mixed and Hybrid Finite Element Methods
• An Observation Concerning Ritz-Galerkin Methods with Indefinite Bilinear Forms
• Some Observations on Generalized Saddle-Point Problems
• A Note on Preconditioning for Indefinite Linear Systems
• Hierarchical Schur complement preconditioner for the stochastic Galerkin finite element methods
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