A Constraint Energy Minimizing Generalized Multiscale Finite Element Method for Parabolic Equations

DOI10.1137/18M1193128zbMath1426.65200arXiv1806.04816OpenAlexW2968667155MaRDI QIDQ5197638

Mengnan Li, Eric T. Chung, Lijian Jiang

Publication date: 19 September 2019

Published in: Multiscale Modeling & Simulation (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1806.04816

zbMATH Keywords

a posteriori error estimatorhigh-contrast porous mediaCEM-GMsFEMmultiscale parabolic equations

Mathematics Subject Classification ID

Flows in porous media; filtration; seepage (76S05) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Error bounds for initial value and initial-boundary value problems involving PDEs (65M15) Multiple scale methods for ordinary differential equations (34E13) Numerical methods for partial differential equations, boundary value problems (65N99)

Related Items (8)

Contrast-independent partially explicit time discretizations for multiscale flow problems ⋮ Online Multiscale Model Reduction for Nonlinear Stochastic PDEs with Multiplicative Noise ⋮ A combined multiscale finite element method based on the LOD technique for the multiscale elliptic problems with singularities ⋮ Convergence of the CEM-GMsFEM for compressible flow in highly heterogeneous media ⋮ Constraint Energy Minimizing Generalized Multiscale Finite Element Method for Convection Diffusion Equation ⋮ Convergence analysis of constraint energy minimizing generalized multiscale finite element method for a linear stochastic parabolic partial differential equation driven by additive noises ⋮ Iterative oversampling technique for constraint energy minimizing generalized multiscale finite element method in the mixed formulation ⋮ Second-order two-scale analysis for heating effect of periodical composite structure

Cites Work

• Generalized multiscale finite element methods (GMsFEM)
• Homogenized behavior of two-phase flows in naturally fractured reservoirs with uniform fractures distribution
• Multiscale finite-volume method for parabolic problems arising from compressible multiphase flow in porous media
• Hierarchical multiscale modeling for flows in fractured media using generalized multiscale finite element method
• Modeling fractures as interfaces: A model for Forchheimer fractures
• The variational multiscale method -- a paradigm for computational mechanics
• A multiscale finite element method for elliptic problems in composite materials and porous media
• Analysis of upscaling absolute permeability
• Implementation of a locally conservative numerical subgrid upscaling scheme for two-phase Darcy flow
• Multi-scale finite-volume method for elliptic problems in subsurface flow simulation.
• Constraint energy minimizing generalized multiscale finite element method
• Least-squares mixed generalized multiscale finite element method
• Model's sparse representation based on reduced mixed GMsFE basis methods
• Multiscale methods for parabolic equations with continuum spatial scales
• Elliptic reconstruction and a posteriori error estimates for fully discrete linear parabolic problems
• Analysis of the heterogeneous multiscale method for parabolic homogenization problems
• Homogenization of Parabolic Equations with a Continuum of Space and Time Scales
• A posteriori error estimates for nonlinear problems. 𝐿^{𝑟}(0,𝑇;𝐿^{𝜌}(Ω))-error estimates for finite element discretizations of parabolic equations
• A POSTERIORIERROR ESTIMATION FOR THE FINITE ELEMENT METHOD-OF-LINES SOLUTION OF PARABOLIC PROBLEMS
• A Posteriori Error Estimation with Finite Element Semi- and Fully Discrete Methods for Nonlinear Parabolic Equations in One Space Dimension
• A posteriori error estimation and adaptivity for degenerate parabolic problems
• A parallel Monte‐Carlo finite‐element procedure for the analysis of multicomponent random media
• Modeling Fractures and Barriers as Interfaces for Flow in Porous Media

This page was built for publication: A Constraint Energy Minimizing Generalized Multiscale Finite Element Method for Parabolic Equations