Edge stabilization for Galerkin approximations of convection?diffusion?reaction problems

By Erik Burman, Peter Hansbo. 2004

362 citations recorded by the source corpus.

Subfields: Computational Mechanics, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/2ccfe2d9ebf2d1af90268c2cff0de5f45a23c9e8

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In Computational Mechanics

In Computational Theory and Mathematics

Citations in the corpus

Isogeometric analysis : CAD, finite elements, NURBS, exact geometry and mesh refinement (2005, background): “Recent, stateof-the-art literature on stabilized methods is presented in [55–66].”
Weak imposition of Dirichlet boundary conditions in fluid mechanics (2007, methodology): “Recent work on stabilized methods is presented in [21, 38, 48, 19, 20, 13, 24, 9, 23, 8, 3, 41].”
The role of continuity in residual-based variational multiscale modeling of turbulence (2007, methodology): “Recent work on stabilized methods is presented in [1,8,9,11,14,18–21,28,33,41–43].”
Finite element methods with symmetric stabilization for the transient convection―diffusion-reaction equation (2009, methodology): “From the analysis in the steady case, see [5, 4], we know that the bilinear form ah(·, ·) satisfies the following coercivity and continuity estimate, where πh denotes the standard L(2)-projection onto Vh: |||vh||| .”
VARIATIONAL DISCRETIZATION FOR OPTIMAL CONTROL GOVERNED BY CONVECTION DOMINATED DIFFUSION EQUATIONS (2009, methodology): “Both approaches use standard finite element discretization with stabilization based on symmetric penalty terms, where local projections (the so called LPS-method) are used in [3], and edge stabilization (see [5]) in [29].”
Grad–div stabilization and subgrid pressure models for the incompressible Navier–Stokes equations (2009, neutral): “[6,10–12].”
An assessment of discretizations for convection-dominated convection–diffusion equations (2011, methodology): “The considered CIP method (6) is the method abbreviated by ES in the numerical studies of [5].”
On spurious oscillations at layers diminishing (SOLD) methods for convection–diffusion equations: Part I – A review (2007, background): “In addition, we want to note that the solutions obtained with J90, BH04 and BE05_2 show, in contrast to all other methods, a smearing of the exponential boundary layer.”
Analysis of a stabilized finite element approximation of the Oseen equations using orthogonal subscales (2008, neutral): “Finally, let us mention the method proposed in [13] to stabilize convection which, like the stabilization of the convective term in (21), does not involve the whole residual of the equation to be solved.”
A unified analysis of algebraic flux correction schemes for convection–diffusion equations (2018, methodology): “[16]) and the local projection stabilization (LPS) method (see [12] for the first application of this method to a convection-dominated equation).”