NUMERICAL HOMOGENIZATION OF A NONLINEARLY COUPLED ELLIPTIC–PARABOLIC SYSTEM, REDUCED BASIS METHOD, AND APPLICATION TO NUCLEAR WASTE STORAGE

DOI10.1142/S0218202513500395zbMath1330.35027OpenAlexW2170447921MaRDI QIDQ2857743

Stella Krell, Antoine Gloria, Thierry Goudon

Publication date: 5 November 2013

Published in: Mathematical Models and Methods in Applied Sciences (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1142/s0218202513500395

zbMATH Keywords

convection-diffusion equationporous mediacoarse graining

Mathematics Subject Classification ID

Theoretical approximation in context of PDEs (35A35) Finite element methods applied to problems in fluid mechanics (76M10) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) Applications to the sciences (65Z05) Homogenization in context of PDEs; PDEs in media with periodic structure (35B27) Homogenization applied to problems in fluid mechanics (76M50)

Related Items (9)

Numerical homogenization: survey, new results, and perspectives ⋮ Homogenization of nonisothermal immiscible incompressible two-phase flow in porous media ⋮ Sensor placement in nuclear reactors based on the generalized empirical interpolation method ⋮ An improved homogenization result for immiscible compressible two-phase flow in porous media ⋮ Homogenization of a model for water-gas flow through double-porosity media ⋮ Homogenization of nonisothermal immiscible incompressible two-phase flow in double porosity media ⋮ Homogenization of MHD flows in porous media ⋮ Homogenization of coupled immiscible compressible two-phase flow with kinetics in porous media ⋮ Homogenization of compressible two-phase two-component flow in porous media

Uses Software

• COUPLEX

Cites Work

• Convergence rates of best \(N\)-term Galerkin approximations for a class of elliptic SPDEs
• The COUPLEX test cases: nuclear waste disposal simulation
• Compact sets in the space \(L^ p(0,T;B)\)
• Homogenization of non-uniformly bounded operators: critical barrier for nonlocal effects
• Global a priori convergence theory for reduced-basis approximations of single-parameter symmetric coercive elliptic partial differential equations
• On existence and uniqueness results for a coupled systems modeling miscible displacement in porous media
• Homogenization of a model of displacement with unbounded viscosity
• A general multipurpose interpolation procedure: The magic points
• APPROXIMATION BY HOMOGENIZATION AND DIFFUSION OF KINETIC EQUATIONS
• ANALYTIC REGULARITY AND POLYNOMIAL APPROXIMATION OF PARAMETRIC AND STOCHASTIC ELLIPTIC PDE'S
• Reduced-Basis Approach for Homogenization beyond the Periodic Setting
• Homogenization and Two-Scale Convergence
• Mathematical Analysis of Miscible Displacement in Porous Medium
• A General Convergence Result for a Functional Related to the Theory of Homogenization
• Mathematical Analysis for Reservoir Models
• An Approximation to Miscible Fluid Flows in Porous Media with Point Sources and Sinks by an Eulerian--Lagrangian Localized Adjoint Method and Mixed Finite Element Methods
• An improved numerical simulator for different types of flows in porous media

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