A mixed finite element for the stokes problem using quadrilateral elements

Farhloul, Mohamed; Fortin, Michel

doi:10.1007/bf02431998

Cited by 5 publications

(5 citation statements)

References 81 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…As a consequence, the postprocessing u * h also satisfies the estimate of Theorem 2.4 and hence converges with order two whenever the solution is smooth enough. These results complement the error estimates obtained in [9,10].…”

Section: This Completes the Proofsupporting

confidence: 86%

“…Note that all the methods achieve optimal orders for L h , p h and that superconvergence takes place for the projection of the error in u. For k = 0 and two dimensions, the method listed in Table 1 as RT k is the mixed method proposed in [9], and that the method listed in Table 3 as RT [k] is the mixed method proposed in [10]; as pointed out in the Introduction, general, convex quadrilaterals were also considered therein.…”

Section: 2mentioning

confidence: 99%

“…It is worth noting that a particular case of the family of methods employing k-th order Raviart-Thomas elements for the approximate velocity gradient is already known. Indeed, the two-dimensional case with k = 0 is nothing but the mixed method proposed in [9] for triangles and in [10] for rectangles; general, convex quadrilaterals were also considered in [10].…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Conditions for superconvergence of HDG methods for Stokes flow

Cockburn

Shi

2012

Math. Comp.

View full text Add to dashboard Cite

We provide an a priori error analysis of a wide class of finite element methods for the Stokes equations. The methods are based on the velocity gradient-velocity-pressure formulation of the equations and include new and old mixed and hybridizable discontinuous Galerkin methods. We show how to reduce the error analysis to the verification of some properties of an elementwise-defined projection and of the local spaces defining the methods. We also show that the projection of the errors only depends on the approximation properties of the projection. We then provide sufficient conditions for the superconvergence of the projection of the error in the approximate velocity. We give many examples of these methods and show how to systematically construct them from similar methods for the diffusion equation.

show abstract

Section: This Completes the Proofsupporting

confidence: 86%

Section: 2mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Conditions for superconvergence of HDG methods for Stokes flow

Cockburn

Shi

2012

Math. Comp.

View full text Add to dashboard Cite

show abstract

“…In this section, we perform a numerical validation of the stabilized PM method (30) applied to the solution of the model problem (22) on the test network geometry depicted in Fig. 8.…”

Section: Numerical Validation Of the Pm Discretizationmentioning

confidence: 99%

“…The above proposed stabilized MFV method is the extension to rectangular elements of the formulation for triangular grids introduced and analyzed in [25,7]. For a similar use of numerical quadrature aimed to construct a finite volume variant of the DM method, we refer to [30] in the case of the advection-diffusion-reaction model problem and to [15] for the approximate solution of the Stokes problem in fluid-dynamics. The MFV method (15) can be written in matrix form as…”

Section: The Stabilized Dual Mixed Finite Volume Approximationmentioning

confidence: 99%

A multiscale thermo-fluid computational model for a two-phase cooling system

Sacco¹,

Carichino²,

Falco³

et al. 2014

Computer Methods in Applied Mechanics and Engineering

View full text Add to dashboard Cite

In this paper, we describe a mathematical model and a numerical simulation method for the condenser component of a novel two-phase thermosiphon cooling system for power electronics applications. The condenser consists of a set of roll-bonded vertically mounted fins among which air flows by either natural or forced convection. In order to deepen the understanding of the mechanisms that determine the performance of the condenser and to facilitate the further optimization of its industrial design, a multiscale approach is developed to reduce as much as possible the complexity of the simulation code while maintaining reasonable predictive accuracy. To this end, heat diffusion in the fins and its convective transport in air are modeled as 2D processes while the flow of the two-phase coolant within the fins is modeled as a 1D network of pipes. For the numerical solution of the resulting equations, a Dual Mixed-Finite Volume scheme with Exponential Fitting stabilization is used for 2D heat diffusion and convection while a Primal Mixed Finite Element discretization method with upwind stabilization is used for the 1D coolant flow. The mathematical model and the numerical method are validated through extensive simulations of realistic device structures which prove to be in excellent agreement with available experimental data

show abstract

A mixed-hybrid finite element method for convection–diffusion problems

Farhloul

Mounim

2005

Applied Mathematics and Computation

View full text Add to dashboard Cite

A mixed finite element for the stokes problem using quadrilateral elements

Cited by 5 publications

References 81 publications

Conditions for superconvergence of HDG methods for Stokes flow

Conditions for superconvergence of HDG methods for Stokes flow

A multiscale thermo-fluid computational model for a two-phase cooling system

A mixed-hybrid finite element method for convection–diffusion problems

Contact Info

Product

Resources

About