Certified reduced basis method in geosciences. Addressing the challenge of high-dimensional problems

DOI10.1007/s10596-019-09916-6zbMath1434.86002OpenAlexW2995223207WikidataQ118177569 ScholiaQ118177569MaRDI QIDQ2187912

Florian Wellmann, Denise Degen, Karen Veroy

Publication date: 3 June 2020

Published in: Computational Geosciences (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10596-019-09916-6

zbMATH Keywords

finite element methodreduced basis methodmodel order reductiongeothermal conductionMOOSE framework

Mathematics Subject Classification ID

Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) Computational methods for problems pertaining to geophysics (86-08)

Related Items (2)

A greedy sensor selection algorithm for hyperparameterized linear Bayesian inverse problems with correlated noise models ⋮ Accurate error estimation for model reduction of nonlinear dynamical systems via data-enhanced error closure

Uses Software

• Gmsh
• rbMIT
• FreeFem++
• PETSc
• FEniCS
• DAKOTA
• Feel++
• libMesh
• redbKIT
• REDBACK
• GemPy
• RBniCS
• MeshIt
• ECLIPSE

Cites Work

• A high-performance parallel implementation of the certified reduced basis method
• Reduced-order modeling for thermal recovery processes
• Model order reduction in porous media flow simulation using quadratic bilinear formulation
• Reduced basis approximation and a-posteriori error estimation for the coupled Stokes-Darcy system
• Adaptive POD model reduction for solute transport in heterogeneous porous media
• Certified reduced basis methods for parametrized elliptic optimal control problems with distributed controls
• A Petrov-Galerkin reduced basis approximation of the Stokes equation in parameterized geometries
• pyMOR -- Generic Algorithms and Interfaces for Model Order Reduction
• Certified Reduced Basis Methods for Parametrized Partial Differential Equations
• Feel++ : A computational framework for Galerkin Methods and Advanced Numerical Methods
• Gmsh: A 3-D finite element mesh generator with built-in pre- and post-processing facilities
• Certified real‐time solution of the parametrized steady incompressible Navier–Stokes equations: rigorous reduced‐basis a posteriori error bounds
• A posteriorierror bounds for reduced-basis approximations of parametrized parabolic partial differential equations
• Reduced Basis Methods for Partial Differential Equations

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