Computer Methods in Applied Mechanics and Engineering
Penalty finite element method for the Navier-Stokes equations
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Cited by (46)
Flow stability and regime transitions on periodic open foams
2024, International Journal of Multiphase FlowA decoupling penalty finite element method for the stationary incompressible MagnetoHydroDynamics equation
2019, International Journal of Heat and Mass TransferAn error analysis of the finite element method overcoming corner singularities for the stationary Stokes problem
2017, Computers and Mathematics with ApplicationsA finite element method for singular solutions of the Navier-Stokes equations on a non-convex polygon
2016, Journal of Computational and Applied MathematicsCitation Excerpt :Also, error estimates and iterative convergence results for the nonlinear equations were shown. In [16] a penalty formulation for the Navier–Stokes equations was analyzed, and in [17] a nonconforming finite element method for the inhomogeneous boundary value problem was constructed. In [18] a stabilization technique allowing the use of equal interpolation for the velocity and pressure was analyzed, and in [19] the mixed formulation of the Navier–Stokes equations with mixed boundary conditions in 2D polygonal domains was constructed.
Dynamic interaction of heat transfer, air flow and disc vibration of disc drives - Theoretical development and numerical analysis
2014, International Journal of Mechanical SciencesCitation Excerpt :In the study of the penalty finite element method for Navier–Stokes equations, it was demonstrated systematically by Codina [46], Carey and Krishnan [47,48] that “In computations with smaller values of ε, roundoff effects due to computation in finite precision are found to be an important consideration” and “Perhaps the only drawback of this approach (of the penalty finite element method) is the ill-conditioning of the stiffness matrix when the penalty parameter ε is very small”. Just theoretically speaking, the solution from the penalty finite element method can converge to its true value when penalty parameter ε goes to zero, whereas the fact is that “These theoretical results presume exact arithmetic, not limited by the finite precision of digital computation” as stated in Carey and Krishnan [47]. As a result, when penalty parameter ε is very small, starting from 10−7 in Table 5, “the roundoff effects” and “the ill-conditioning of the stiffness matrix” emerge and cause the ‘stiffness’ matrix to become close to singular or badly scaled and some inaccurate results are obtained.
Numerical study on permeate flux enhancement by spacers in a crossflow reverse osmosis channel
2006, Journal of Membrane Science