Finite element stabilization parameters computed from element matrices and vectors

Tezduyar, Tayfun E.; Osawa, Yasuo

doi:10.1016/s0045-7825(00)00211-5

Cited by 374 publications

(279 citation statements)

References 14 publications

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“…The last term on the right hand side of Equation (52) is introduced to stabilize the incompressibility equation as discussed in [25]. The remaining stabilizing terms in Equations (52) and (53) can be derived by various techniques including a least squares procedure.…”

Section: A Stabilized Finite Element Scheme For the Momentum Equationsmentioning

confidence: 99%

“…where n en is the number of nodes in the element, N e α is the basis function associated with the local node α, and s is the unit vector in the direction of the local velocity [23,24,25]. The element h # on the other hand is defined to be the diameter of the circle which is area equivalent to the element.…”

Section: A Stabilized Finite Element Scheme For the Momentum Equationsmentioning

confidence: 99%

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A stabilized volume‐averaging finite element method for flow in porous media and binary alloy solidification processes

Zabaras

Samanta

2004

Numerical Meth Engineering

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SUMMARYA stabilized equal-order velocity-pressure finite element algorithm is presented for the analysis of flow in porous media and in the solidification of binary alloys. The adopted governing macroscopic conservation equations of momentum, energy and species transport are derived from their microscopic counterparts using the volume-averaging method. The analysis is performed in a single-domain with a fixed numerical grid. The fluid flow scheme developed includes SUPG (streamline-upwind/PetrovGalerkin), PSPG (pressure stabilizing/Petrov-Galerkin) and DSPG (Darcy stabilizing/PetrovGalerkin) stabilization terms in a variable porosity medium. For the energy and species equations a classical SUPG-based finite element method is employed. The developed algorithms were tested extensively with bilinear elements and were shown to perform stably and with nearly quadratic convergence in high Rayleigh number flows in varying porosity media. Examples are shown in natural and double diffusive convection in porous media and in the directional solidification of a binary-alloy.

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Section: A Stabilized Finite Element Scheme For the Momentum Equationsmentioning

confidence: 99%

Section: A Stabilized Finite Element Scheme For the Momentum Equationsmentioning

confidence: 99%

A stabilized volume‐averaging finite element method for flow in porous media and binary alloy solidification processes

Zabaras

Samanta

2004

Numerical Meth Engineering

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“…A classical step-size controller is used for time step selection with maximum increase and decrease factors of two and one-tenth, respectively [69, p. 168]. For stabilized CG approximations, the evaluation of τ and ν c is lagged a time step after an initial startup phase in an effort to simplify the nonlinear solves [70]. ∆t is decreased by a factor of ten when a nonlinear solver failure is encountered.…”

Section: Time Integrationmentioning

confidence: 99%

Locally conservative, stabilized finite element methods for variably saturated flow

Kees

Farthing

Dawson

2008

Computer Methods in Applied Mechanics and Engineering

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“…with the help of element matrix and vector norms [24], the Green's function of the element [12], mathematical error analysis [4,5,16], or model equations [2,9,17].…”

Section: The Stabilisation Parametermentioning

confidence: 99%

Meshfree Petrov-Galerkin Methods for the Incompressible Navier-Stokes Equations

Fries

Matthies

Meshfree Methods for Partial Differential Equations II

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Meshfree stabilised methods are employed and compared for the solution of the incompressible Navier-Stokes equations in Eulerian formulation. These PetrovGalerkin methods are standard tools in the FEM context, and can be used for meshfree methods as well. However, the choice of the stabilisation parameter has to be reconsidered. We find that reliable and successful approximation with standard formulas for the stabilisation parameter can only be expected for shape functions with small supports or dilatation parameters.

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Finite element stabilization parameters computed from element matrices and vectors

Cited by 374 publications

References 14 publications

A stabilized volume‐averaging finite element method for flow in porous media and binary alloy solidification processes

A stabilized volume‐averaging finite element method for flow in porous media and binary alloy solidification processes

Locally conservative, stabilized finite element methods for variably saturated flow

Meshfree Petrov-Galerkin Methods for the Incompressible Navier-Stokes Equations

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