A finite element pressure gradient stabilization¶for the Stokes equations based on local projections

By Roland Becker, Malte Braack. 2001

423 citations recorded by the source corpus.

Subfields: Computational Mechanics, Computational Theory and Mathematics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/109094bab2ba1791c635ae9a6b3615b02d92a05a

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In Computational Mechanics

In Computational Theory and Mathematics

In Statistical and Nonlinear Physics

Citations in the corpus

A stabilized finite element method based on two local Gauss integrations for the Stokes equations (2008, methodology): “For the local pressure projection method, we can review the work of Becker and Braack [2], Brezzi and Fortin [7], Bochev and Dohrmann [311], Layton [17], Erik Burman [8] and Silvester [20].”
FAST ITERATIVE SOLVERS FOR CONVECTION-DIFFUSION CONTROL PROBLEMS ∗ (2013, methodology): “Here we employ the adjoint-consistent local projection stabilization approach described by [1, 2, 5] which ensures that the discretize and optimize steps commute.”
Analysis of a stabilized finite element approximation of the Oseen equations using orthogonal subscales (2008, neutral): “In this situation, and when the meshes are made of patches of 2 × 2 quadrilaterals (in 2D), it is shown in [2] that the projections can be computed locally on each patch.”
A unified stabilized method for Stokes' and Darcy's equations (2007, neutral): “FINITE ELEMENT CENTER PREPRINT 2002–15”
A simple pressure stabilization method for the Stokes equation (2007, methodology): “Alternative formulations have been developed in [4] where instead the pressure gradient is introduced as an additional variable (three-field formulation) [5], where a stabilization based on local projections between two different spaces is used, and [6] where the jump of the normal derivative over e”
A UNIFIED CONVERGENCE ANALYSIS FOR LOCAL PROJECTION STABILISATIONS APPLIED TO THE OSEEN PROBLEM (2007, methodology): “In applications, the projection P H : Y h → Y 2 h in the two-level approach has been often chosen as the global Lagrange interpolant I 2 h,r into Y 2 h [4,7–9,11,32].”
SOLUTIONS OF 3D NAVIER-STOKES BENCHMARK PROBLEMS WITH ADAPTIVE FINITE ELEMENTS (2006, methodology): “We use local projection stabilization (LPS) as introduced in [3, 4] for both types for stabilization.”
Stabilization of Low-order Mixed Finite Elements for the Stokes Equations (2004, methodology): “One example, motivated by fractional step algorithms for time-dependent problems, is the pressure gradient projection (PGP) method (see [6, 7, 13]) and the related local pressure gradient stabilization (LPS) method [4].”
Robust Globally Divergence-Free Weak Galerkin Methods for Stokes Equations (2016, methodology): “, Galerkin least-square methods [5, 7, 17, 37], pressure projection methods [8,14,18], pressure gradient projection methods [13,30], and local projection stabilized methods [6, 39,51].”
Stabilization of local projection type applied to convection-diffusion problems with mixed boundary conditions. (2008, methodology): “This method has been proposed for the Stokes problem in [3].”
Characteristic stabilized finite element method for the transient Navier–Stokes equations (2010, neutral): “Simultaneously, other stabilized mixed finite element methods involving non-residual stabilization have also been proposed [25] [26] [27] [28].”