Stabilization of Low-order Mixed Finite Elements for the Stokes Equations

By Pavel B. Bochev, Clark R. Dohrmann, Max D. Gunzburger. SIAM Journal on Numerical Analysis, 2004

457 citations recorded by the source corpus.

Subfields: Computational Mechanics, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/47be4e317d4dcbbf1b70c781394e49c1dbf7e538

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computational Mechanics

In Numerical Analysis

Citations in the corpus

Local projection stabilization for advection--diffusion--reaction problems: One-level vs. two-level approach (2009, methodology): “An attractive alternative to this approach is the parameter-free LPS proposed in [5] where not the pressure gradient but the pressure itself is projected.”
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.”
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].”
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.”
Grad–div stabilization and subgrid pressure models for the incompressible Navier–Stokes equations (2009, unknown): “[5]):”
Performance of mixed formulations for the particle finite element method in soil mechanics problems (2016, methodology): “The stabilization method used is the so-called polynomial pressure projection (PPP) previously applied to stabilize Stokes equations [4,11].”
A stabilized assumed deformation gradient finite element formulation for strongly coupled poromechanical simulations at finite strain (2013, methodology): “On the other hand, another pressure projection technique originally developed for the stationary Stokes’ equation in [38] has been adopted to small strain poromechanics problems in [18].”
Stabilized low-order finite elements for frictional contact with the extended finite element method (2010, background): “The second set deals with frictional contact and assesses the performance of the stabilized penalty formulation.”