A Petrov-Galerkin multiscale hybrid-mixed method for the Darcy equation on polytopes

DOI10.1007/s40314-023-02304-yzbMath1524.65796OpenAlexW3010983162MaRDI QIDQ6103362

No author found.

Publication date: 2 June 2023

Published in: Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s40314-023-02304-y

zbMATH Keywords

Darcy equationPetrov-Galerkin formulationmultiscale hybrid-mixed method

Mathematics Subject Classification ID

PDEs in connection with fluid mechanics (35Q35) Flows in porous media; filtration; seepage (76S05) Error bounds for boundary value problems involving PDEs (65N15) Stability and convergence of numerical methods for boundary value problems involving PDEs (65N12) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Integro-partial differential equations (35R09)

Cites Work

• A family of Multiscale Hybrid-Mixed finite element methods for the Darcy equation with rough coefficients
• Numerical multiscale methods for a reaction-dominated model
• An optimal Poincaré inequality for convex domains
• The heterogeneous multiscale methods
• Stabilization arising from PGEM: A review and further developments
• The variational multiscale method -- a paradigm for computational mechanics
• Theory and practice of finite elements.
• A multiscale hybrid method for Darcy's problems using mixed finite element local solvers
• The multiscale hybrid mixed method in general polygonal meshes
• Consistent Local Projection Stabilized Finite Element Methods
• Poincare constants for finite element stars
• Localization of elliptic multiscale problems
• Generalized Finite Element Methods: Their Performance and Their Relation to Mixed Methods
• Primal Hybrid Finite Element Methods for 2nd Order Elliptic Equations
• Poincaré--Friedrichs Inequalities for Piecewise H¹ Functions
• Stability analysis for the virtual element method
• Mixed Finite Element Methods and Applications
• Convergence of a Nonconforming Multiscale Finite Element Method
• On a Multiscale Hybrid-Mixed Method for Advective-Reactive Dominated Problems with Heterogeneous Coefficients
• Multiscale Hybrid-Mixed Method
• A Multiscale Mortar Mixed Finite Element Method

This page was built for publication: A Petrov-Galerkin multiscale hybrid-mixed method for the Darcy equation on polytopes