Finite Element Methods and Navier-Stokes Equations

Cuvelier, Claude; Segal, A.; Steenhoven, A.A. van

doi:10.1007/978-94-010-9333-0

Cited by 255 publications

(185 citation statements)

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“…It can also be extended to general threedimensional domains, where the construction of the locally-divergence basis is more complicated (cf. Section 9.3 of [10]). …”

Section: Discussionmentioning

confidence: 99%

“…For a simply connected Ω, there exists a completely local basis for V h consisting of vector fields tangential to the edges of T h and vector fields representing rotations around the vertices of T h [18,10]. For a multiply connected domain, the basis of V h involves vector fields along cuts that reduce Ω to a simply connected domain, in addition to local vector fields.…”

Section: Locally Divergence-free Vector Fields On Graded Meshesmentioning

confidence: 99%

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A locally divergence-free nonconforming finite element method for the time-harmonic Maxwell equations

Brenner

Sung

2006

Math. Comp.

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Abstract. A new numerical method for computing the divergence-free part of the solution of the time-harmonic Maxwell equations is studied in this paper. It is based on a discretization that uses the locally divergence-free CrouzeixRaviart nonconforming P 1 vector fields and includes a consistency term involving the jumps of the vector fields across element boundaries. Optimal convergence rates (up to an arbitrary positive ) in both the energy norm and the L 2 norm are established on graded meshes. The theoretical results are confirmed by numerical experiments.

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“…It can also be extended to general threedimensional domains, where the construction of the locally-divergence basis is more complicated (cf. Section 9.3 of [10]). …”

Section: Discussionmentioning

confidence: 99%

Section: Locally Divergence-free Vector Fields On Graded Meshesmentioning

confidence: 99%

A locally divergence-free nonconforming finite element method for the time-harmonic Maxwell equations

Brenner

Sung

2006

Math. Comp.

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“…The Stokes equations are solved with SIMPLE (Patankar, 1980). Peter van Keken (UM) uses a finite element approach based on the Sepran software (Cuvelier et al, 1986)(dutita0.twi.tudelft.nl/ sepran/sepran.html). Linear triangles with SUPG (using the double asymptotic approach) are used for the heat equation.…”

Section: Contributing Codesmentioning

confidence: 99%

A community benchmark for subduction zone modeling

Keken

Currie

King

et al. 2008

Physics of the Earth and Planetary Interiors

199

144

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“…html). The momentum equation is solved on quadratic triangular elements using a penalty function method [Cuvelier et al, 1986]. The strain rate dependence of viscosity necessitates iterative solution of the momentum and viscosity equations.…”

Section: Convection Equationsmentioning

confidence: 99%

Development of finite strain in the convecting lower mantle and its implications for seismic anisotropy

2003

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[1] Seismological observations have revealed patches of seismic anisotropy in regions related to mantle upwelling and paleosubduction within an otherwise isotropic lower mantle. A combination of numerical modeling and mineral physics is used to constrain the source of anisotropy in these regions in an effort to better understand lower mantle dynamics and mineral physics. Specifically, it is investigated whether lattice-preferred orientation (LPO) can explain the anisotropy observed in regions of paleosubduction. Since LPO is caused by dislocation creep and is destroyed by diffusion creep, we can develop deformation mechanism maps to determine which regions allow for the development of a mineral fabric. Strain is then calculated in these regions and is related to mineral physics experiments combined with high-pressure elastic constants of lower mantle minerals in order to assess the predicted seismic anisotropy. Uncertainties in rheological parameters such as the transition stress between dislocation creep and diffusion creep necessitate a full evaluation of the parameter range. The effect of variations in transition stress, activations parameters, and strength of slabs on fabric development is investigated. It is shown that LPO is a likely candidate for the cause of lowermost mantle anisotropy in regions of paleosubduction.

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Finite Element Methods and Navier-Stokes Equations

Cited by 255 publications

References 0 publications

A locally divergence-free nonconforming finite element method for the time-harmonic Maxwell equations

A locally divergence-free nonconforming finite element method for the time-harmonic Maxwell equations

A community benchmark for subduction zone modeling

Development of finite strain in the convecting lower mantle and its implications for seismic anisotropy

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