A stabilized finite element method for the Stokes problem based on polynomial pressure projections

By Clark R. Dohrmann, Pavel B. Bochev. 2004

419 citations recorded by the source corpus.

Subfields: Computational Mechanics, Electrical and Electronic Engineering

View Paper: https://www.semanticscholar.org/paper/2065b1ee6cf873c4c26aecae3ca373438746e2ff

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In Computational Mechanics

In Electrical and Electronic Engineering

Citations in the corpus

Stabilization of Low-order Mixed Finite Elements for the Stokes Equations (2004, methodology): “In this paper, we analyze a new, nonresidual-based approach to the stabilization of low-order mixed finite element discretizations of the Stokes equations, further developing the idea of polynomial-pressure-projection–based stabilization that was presented and studied computationally in [14].”
On the numerical modeling of granular material flows via the Particle Finite Element Method (PFEM) (2015, methodology): “The plastic flow condition is assumed nearly incompressi-5 ble, so a pu− mixed formulation, with a stabilization of the pressure term via the Polynomial 6 Pressure Projection (PPP), is employed.”
Characteristic stabilized finite element method for the transient Navier–Stokes equations (2010, positive): “[31] is used in our experiments.”
Pressure projection stabilizations for Galerkin approximations of Stokes' and Darcy's problem (2008, methodology): “The same ideas have been exploited more recently in the work by Dohrmann and Bochev [5] and Layton [6].”
On stabilized finite element methods for the Stokes problem in the small time step limit (2007, methodology): “Another alternative is to use non-residual stabilized methods such as pressure projection [4, 18], or pressure jump [41, 42] stabilized methods, or a stable mixed method.”
Stabilized low-order finite elements for frictional contact with the extended finite element method (2010, methodology): “[6,7,16] quantified the deficiency of some of these low-order mixed finite elements, and proposed a stabilized method aimed at addressing this deficiency.”
Multiscale and Stabilized Methods (2007, background): “See, for example, Codina and Blasco (2000a, 2000b), and Bochev and Dohrman (2004).”
Least-Squares Finite Element Methods (2009, background): “, for the Stokes problem, stabilized FEMs [4]–[5], [6], [12], [15], [29], [30], [36], [37], [44] recover advantages 2 and 3 but fail to recover advantage 4c and often lose advantage 4b.”
FEAP - - A Finite Element Analysis Program (2011, methodology): “Several schemes have been proposed, however, a simple and effective method is to modify the functional by adding a term [8]”
A simple pressure stabilization method for the Stokes equation (2007, methodology): “Dohrmann C, Bochev P.”