Stabilization of incompressibility and convection through orthogonal sub-scales in finite element methods

By Ramon Codina. 2000

440 citations recorded by the source corpus.

Subfields: Computational Mechanics, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/c0b9a4b4eb42315c06ea3cfa3228f72c0bfe378b

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In Computational Mechanics

In Computational Theory and Mathematics

Citations in the corpus

Softening, localization and stabilization: capture of discontinuous solutions in J2 plasticity (2004, background): “In the cases of elastic incompressibility or smooth widespread, non-localizing, plastic responses, they are able to preclude the pressure oscillations that arise if the standard Galerkin method is used (see References [25, 26]).”
A residual correction method based on finite calculus (2003, methodology): “…is introduced and shown to give alternative solution, including one which leads to the Brezzi-Pitkäranta (Brezzi and Pitkäranta, 1984) or Galerkin least squares (Hughes et al., 1989) result of adding a Laplacian term as well as an orthogonal sub-scale form (Codina, 2000; Codina and Blasco, 2000).”
Finite element modeling of quasi-brittle cracks in 2D and 3D with enhanced strain accuracy (2017, methodology): “The stabilization procedure consists in the modification of the discrete variational form using the Orthogonal Subscales Method, introduced in [63] within the framework of the Variational Multiscale Stabilization methods [64, 65], and adopted herein.”
Analysis of a stabilized finite element approximation of the Oseen equations using orthogonal subscales (2008, neutral): “These results are very similar to those obtained in [15] with the same test for the nonlinear Navier–Stokes equations.”
Mixed linear/linear simplicial elements for incompressible elasticity and plasticity (2003, background): “It was argued in [20] that a very natural choice for the unknown sub-grid space fVh is the space orthogonal to the finite element space, referred to hereafter asVh .”
Pressure Stability in Fractional Step Finite Element Methods for Incompressible Flows (2001, methodology): “... and has the same stability properties as the case D 1. This stabilizing term can be thought of as a least-squares form of the component of the pressure gradient orthogonal to the finite element space, nC1 3 D rpnC1 h nC1 h . If this allows the stabilization of the pressure, the idea that natural”
A low order Galerkin finite element method for the Navier–Stokes equations of steady incompressible flow: a stabilization issue and iterative methods (2002, methodology): “Although this alteration of the basic Galerkin method (5) is not new and can be found in [13,17,33,46], we concentrate on this issue for the following reasons: Neither physical nor numerical contents of it seems has been clearly understood; The cited references give different recipes for choosing ‘‘”
ON THE ORTHOGONAL SUB-GRID SCALE PRESSURE STABILIZATION IN FINITE DEFORMATION J2 PLASTICITY (2004, neutral): “[18] A. Maniatty, Y. Liu, O. Klaas, M.S. Shephard, Stabilized finite element method for viscoplastic flow: formulation and a simple progressive solution strategy, Computer Methods in Applied Mechanics and Engineering 190 (2001) 4609-4625 [19] A. Maniatty, Y. Liu, O. Klaas, M.S. Shephard, Higher orde”
Assessment of variational multiscale models for the large eddy simulation of turbulent incompressible flows (2015, background): “The first option, already considered in [11,12,18] and named Algebraic Subgrid Scale (ASGS) in [21], is to take the subscales in the space of the residuals, that is, P := I.”
Finite calculus formulation for incompressible solids using linear triangles and tetrahedra (2004, methodology): “This method was first proposed by Codina [15, 16 ] for the stabilization of convection and incompressibility effects in fluid flow problems.”
Numerical modeling of friction stir welding processes (2013, methodology): “The OSS technique, originally developed to fulfil the incompressibility condition in CFD problems (see [26], [28], [27]), has been exploited in the solid mechanics context to deal with elastic incompressibility and J2-plasticity (isochoric) problems (see.”
A stabilized formulation for incompressible elasticity using linear displacement and pressure interpolations (2002, methodology): “This idea was first introduced by Codina in [2] as an extension of a stabilization method formulated for the Stokes problem in [4].”