A stabilized mixed finite element method for Darcy flow based on a multiscale decomposition of the solution

By K. Nakshatrala, D. Turner, Keith D. Hjelmstad, Arif Masud. 2006

336 citations recorded by the source corpus.

Subfields: Computational Mechanics, Computational Theory and Mathematics, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/c446b3fadbf51c0c478f5c40aae86a22e9fa8dbe

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In Computational Mechanics

In Computational Theory and Mathematics

In Mechanics of Materials

Citations in the corpus

Analysis of a new augmented mixed finite element method for linear elasticity allowing $\mathbb{RT}_0$-$\mathbb{P}_1$-$\mathbb{P}_0$ approximations (2006, methodology): “In addition, stabilized mixed finite element methods for related problems, including Darcy flow, incompressible flows, plates, and shells, can be seen in [2, 9, 15, 18, 21, 26,27, 29, 31].”
Topology optimization of creeping fluid flows using a Darcy–Stokes finite element (2006, methodology): “The Babuska–Brezzi condition for the Stokes and Darcy equations is circumvented by using the stabilizations of Hughes et al. [18] and Masud and Hughes [19], respectively.”
Design of maximum permeability material structures (2007, methodology): “We prefer the approach of Masud and Hughes [26] as it allows for equal-order interpolations of the velocity and pressure fields, just as with the stabilized Stokes finite elements.”
Combining a level‐set method and a mixed stabilized P1/P1 formulation for coupling Stokes–Darcy flows (2012, background): “The justification of this choice and further details can be found in [8, 18].”
A unified stabilized method for Stokes' and Darcy's equations (2007, neutral): “FINITE ELEMENT CENTER PREPRINT 2002–15”
A multiscale finite element method for the incompressible Navier-Stokes equations (2006, methodology): “Employing this method, hereon termed as the Hughes variational multiscale (HVM) method, Masud and co-workers developed multiscale/stabilized formulations for the linearized incompressible Navier–Stokes equations [28], the advection–diffusion equation [32], the convective–diffusive heat transfer [1],”
A multiscale/stabilized finite element method for the advection–diffusion equation (2004, positive): “In fact the question one needs to consider is as follows: Is it possible to capture all the essential features in the solution, both coarse and fine, while still using cruder meshes? In other words, is it possible to develop highly accurate numerical schemes on cruder discretizations? Taking this li”
Navier-Stokes/Darcy Coupling: Modeling, Analysis, and Numerical Approximation (2009, methodology): “In this context we cite also the recent work [96] which presents a new stabilized MFE method without mesh-dependent parameters, and the comparative study [77] concerning the numerical reliability of MFE and MHFE methods applied to porous media flows under the influence of mesh parameters and medium ”
Pressure projection stabilizations for Galerkin approximations of Stokes' and Darcy's problem (2008, neutral): “The example we propose is taken from [19] and has the exact solution p = sin(2πx) sin(2πy) with p = 0 on ∂ .”
A residual based a posteriori error estimator for an augmented mixed finite element method in linear elasticity (2006, methodology): “The resulting augmented method, which is easily generalized to 3D, can be viewed as an extension to the elasticity problem of the non-symmetric procedures utilized in [8] and [11].”